Papers

Building on the established one-particle formula for the Araki relative entropy of coherent states, we study how its value acquires a nontrivial dependence on the mass of the scalar field. For a localized vector $h$ belonging to the standard subspace $H_m$ of the one-particle Hilbert space, the known quadratic-form expression is: $S_{H_m}(h)=-\langle h,\log\delta_{H_m}\,h\rangle$. Our contribution is to construct explicitly a mass-indexed family of vectors of the wedge standard subspace on which this expression is evaluated. The mass-shell map $h_m=E_mf$ organizes four structural conditions on rapidity representatives—on-shell dependence, a controlled massless boundary value, decay for large real rapidity, and Bisognano–Wichmann strip analyticity—and we exhibit an entire rapidity wave function, built from a doubled light-cone phase, two sinc factors, and a Gaussian pair, that satisfies them together with the sharp localization criterion: Hardy-type $L^2$ control throughout the Bisognano–Wichmann strip and the exact Tomita boundary relation. The family therefore belongs to $H_m(\W_R)$ for every $m>0$, and its Araki relative entropy is finite and strictly positive, with an exact spectral representation that makes positivity manifest. The entropy is strongly suppressed at large mass, attains a maximum at intermediate mass in $1+1$ dimension, and converges to a finite value along the modular flow as $m\to0^+$. The construction extends fiberwise to $1{+}d$ dimensions through the transverse mass.

The Seiberg-Witten prepotential of four-dimensional $\mathcal{N}=2$ gauge theory can be reached by two recursions of very different nature, and this thesis compares them explicitly. The first part is a self-contained review of the microscopic side: the ADHM construction as a hyperkähler quotient, the supersymmetric measure on the instanton moduli space, Seiberg-Witten theory, and the one- and two-instanton contributions computed by non-commutative resolution and localisation. The second part introduces the $\Omega$-background and Nekrasov's partition function, and uses the AGT correspondence to turn Zamolodchikov's recursion for Virasoro conformal blocks into a recursion for the instanton partition function. For pure $SU(2)$, this recursion is run up to five instantons, including the first corrections in $\epsilon_1,\epsilon_2$. In the last part, the same quantities are obtained from the Eynard-Orantin topological recursion on the Seiberg-Witten curve, which yields the Taylor expansion of the prepotential around an arbitrary point of the Coulomb branch. For pure $SU(2)$ we give the Bergman kernel and the $B$-periods of $\omega_{0,3}$, $\omega_{0,4}$ and $\omega_{1,1}$ in closed form. They reproduce the instanton series generated by Zamolodchikov's recursion, remain valid at strong coupling, where they detect the massless monopole, and at genus one give the first correction to the self-dual $\Omega$-background. The two recursions are thus complementary: one is exact in the vacuum expectation value and perturbative in the instanton number, the other is exact in the instanton parameter and perturbative around a fixed vacuum. We formulate a conjecture relating the $B$-periods of $\omega_{g,n}$ to the derivatives of the genus-$g$ free energy, and list open problems.

We construct a classical formulation of gravity in terms of the vierbein that makes the Hilbert action polynomial in gravitational perturbations and identify some matter models that admit a polynomial coupling to such perturbations as well. We introduce the density vierbein variables that factorize the inverse metric density while retaining an explicit local Lorentz frame. With the introduction of a new auxiliary field, one can construct an action that is polynomial in such variables and their perturbations. Constructed the BRST complex for the model and derived propagators and interaction rules. In four dimensions, a scalar field with the canonical kinetic term and a potential admits a finite number of coupling terms with the density vierbein perturbations. Among all Horndeski gravity models, only a narrow subclass admits a polynomial coupling to the density vierbein perturbations. For instance, the Einstein–scalar–Gauss–Bonnet model always has an infinite tower of interactions with the density vierbein perturbation. Similarly, the standard kinetic term for the Dirac fermions and the standard kinetic term for a vector field both admit an infinite tower of interactions. Consequently, the density vierbein variables provide a great simplification for scalar-gravitational couplings, but the simplification is not strong enough to produce a realistic model with a finite number of matter-gravity terms.

We study the Hagedorn transition of the single-winding Dutta-Gopakumar unitary matrix model at finite rank $N$. Its Schur expansion is a sum of Plancherel probabilities restricted by the finite-rank wall on the number of rows, and the Vershik-Kerov-Logan-Shepp limit shape reaches this wall when the number of boxes equals $N^2/4$. Two scaling windows around the Hagedorn point resolve the wall at different scales. In the outer window the Baik-Deift-Johansson theorem gives a Tracy-Widom crossover, and summing it identifies Liu's critical free-energy coefficient with the first moment of the GUE Tracy-Widom distribution. In the inner window the same sum determines the canonical probability law of the Polyakov loop at the Hagedorn point: the normalized loop $\mathrm{tr}\,U/N$ is uniformly distributed on a disk of radius one half, so the order parameter does not self-average at large $N$. The intensity $|\mathrm{tr}\,U|^2/N^2$ has the same limiting law as the Schur degree $n/N^2$: at the Hagedorn point the canonical degree weights become asymptotically equal below the macroscopic finite-rank wall. Under the partial-deconfinement dictionary the uniform disk becomes a linear probability density for the deconfined color fraction, and its fully deconfined endpoint is the Young-diagram endpoint of Berenstein and Yan. The Tracy-Widom mean also fixes the first finite-$N$ correction to the Polyakov-loop Laplace transform and to all of its fixed radial moments. Bessel-Toeplitz evaluations up to $N = 100$ confirm the free-energy coefficient, the uniform law, and the predicted correction.

In this work, a QCD-inspired effective model describes dark-state interference in a confined three-state system with two low-energy $Q\overline{Q}$ states, $|1\rangle$ and $|2\rangle$, and a gluon-excited hybrid state, $|H\rangle$. A stationary chromoelectric flux-tube background enters the unperturbed Hamiltonian, while a time-dependent chromoelectric perturbation couples $|1\rangle$ and $|2\rangle$ to $|H\rangle$ in a $\Lambda$-type configuration. Under two-photon\footnote{We retain standard terms like “two-photon” from the EIT literature only by mathematical analogy, but they do not refer to electromagnetic photons but to the effective frequencies and energy mismatches of chromoelectric perturbations and gluonic excitations that connect confined states.} resonance and within a Markovian Gorini-Kossakowski-Sudarshan-Lindblad master equation, the system forms a coherent superposition that decouples from $|H\rangle$, strongly suppressing the steady-state probe susceptibility $\operatorname{Im}\chi_{\text{CE}}$ as lower-state decoherence vanishes. A phenomenological non-Abelian correction to the hybrid energy mainly shifts and reshapes the transparency window rather than creating the interference itself. The model is not a first-principles QCD calculation of medium opacity but a controlled effective link between dark-state interference in quantum optics and reduced confined color dynamics.

We describe in explicit detail the rich relationship between division algebras, split composition algebras, triality, Clifford algebras, spinors, triality Lie algebras, generalized reflections, exceptional magic square Lie algebras, triality eigenspaces, 3-symmetric spaces, Vinberg theta algebras, and Exceptional Unification in particle physics.

We construct first-order ladder operators for spin-$\frac{1}{2}$ Dirac fields and transverse, $\gamma$-traceless spin-$\frac{3}{2}$ Rarita–Schwinger fields on maximally symmetric spaces using non-isometric closed conformal Killing vectors. For both spins, we find three distinct operators: two of them, $\mathcal{D}$ and $\mathcal{D}^{s}$, shift the conformal label as $\Delta \to \Delta \pm 1$, while a third operator, $\widetilde{\mathcal{D}}$, reverses the sign of the Dirac eigenvalue at fixed $\Delta$. The latter exists in arbitrary dimensions and reduces to the standard infinitesimal conformal transformation of a primary spinor when acting on massless spin-$\frac{1}{2}$ fields. On $S^N$, the ladder operators relate neighboring fermionic harmonics and generate the spinor tower from Killing-spinor seeds. In Lorentzian signature, we study their action on de Sitter mode spaces. In $dS_4$, the spin-$\frac{3}{2}$ ladders connect the zero-Dirac-mass sector with the fermionic gauge points $M=\pm i/\ell$, while $\widetilde{\mathcal{D}}$ extends to arbitrary mass the conformal-like transformation previously identified for the gauge field. We explicitly present the spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ fermionic harmonics on spheres as well as the de Sitter mode solutions. Finally, we derive the Casimir operators on $S^3$, $dS_3$, and $dS_4$ corresponding to SO(4), SO(3,1) and SO(4,1), and relate their eigenvalues for UIRs to the allowed masses in the fermionic field equations. These results provide a unified geometric framework relating conformal Killing geometry, fermionic Dirac-type spectra, and the representation theory of maximally symmetric spaces.

Two-color QCD provides a unique first-principles laboratory for strongly interacting matter at finite baryon density, where a diquark condensate realizes a baryonic superfluid. We investigate the internal physics of its quantized superfluid vortices in the chiral limit. We find that a vortex localizes an exact and normalizable $S^3\simeq SU(2)$ family of pion modes. Remarkably, the bulk Wess–Zumino–Witten (WZW) term induces a quantized WZW term for these modes, driving the vortex theory in the infrared to the $SU(2)_1$ WZW conformal field theory with central charge $c=1$. Thus a strongly coupled conformal theory emerges on a vortex in a nonconformal bulk theory. The mechanism extends to pseudoreal $Sp(2N)$ gauge theories, where the corresponding minimal vortex theory flows to $SU(2)_N$, with the level directly encoding the microscopic anomaly coefficient.

Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh (SK) formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed $SU(2)$ noise vertices pass a nontrivial continuum fourth-order positivity test.

We compute mutual information for general spacetime regions using Sorkin's Gaussian field formalism. We show that this construction is naturally based on the reduced space of smearings that generate independent fields, making manifest that in QFTs with stress tensor the local algebras generated by regions sharing the same causal completion. We test the method for a Weyl fermion, the chiral current, and massless and massive real scalar fields across various spacetime regions in 1+1 Minkowski space. Across all cases, distinct spacelike-separated spacetime regions sharing the same causal completion yield identical mutual information. This formalism provides a setting in which to test the timelike tube theorem. Indeed, we observe that the mutual information of a timelike lens approaches that of its enveloping diamond as the cutoff is increased, offering a direct numerical verification of the theorem. In all the considered cases, our results agree with known continuum and spatial-lattice results. Finally, this work establishes a natural framework for studying entanglement measures in generalized free field theories, a task that is impractical within other existing prescriptions.

We consider correlation functions of massless fields in three-dimensional Anti-de Sitter spacetime. Using embedding-space spinors akin to spinor helicity variables, we show that masslessness implies holomorphicity. We perform a deformation of the spinors, analogous to the BCFW shift for flat-space amplitudes, to bootstrap correlation functions of Chern-Simons theory in the bulk. We show that the resulting recursion relations in the bulk ${\rm AdS}_3$ are equivalent to the usual ${\rm CFT}_2$ Ward identities for the boundary conserved currents. The double copy of those recursion relations is equivalent to the Ward identities for the stress-energy tensor. Our findings illustrate how modern amplitude techniques can shed new light on CFT correlators, and provide a novel interpretation of fundamental results in two-dimensional conformal field theory.

We study invertible phases protected by non-onsite symmetries carrying nontrivial lattice anomaly indices. While lattice anomalies are usually viewed as obstructions to symmetric short-range-entangled (SRE) states, we show that anomalous lattice symmetries can nevertheless admit invertible phases that are not SRE, and can moreover shift the set of symmetry-compatible invertible phases. In particular, we consider a fermionic $\mathbb Z_4^F$ symmetry in (2+1) dimensions. For an onsite $\mathbb Z_4^F$ symmetry, symmetric invertible phases have integer chiral central charge $c_-\in\mathbb Z$, whereas a non-onsite symmetry with nontrivial lattice anomaly index obstructs all such phases despite having trivial continuum 't Hooft anomaly. We resolve this by constructing an exact exponentially quasi-local $\mathbb Z_4^F$ symmetry of a $p+ip$ superconductor with $c_-=1/2$. We compute its lattice anomaly, and find that the symmetry indeed forbids $c_-\in \mathbb{Z}$ invertible states. The allowed invertible phases are consequently shifted to $c_-\in\mathbb Z+1/2$. By gauging the fermion parity of the $p+ip$ superconductor, one obtains an Ising topological order enriched by a $\mathbb Z_4$ symmetry. We describe the corresponding symmetry structure in terms of a fusion 2-category. We further show that the $p+ip$ state admits an enlarged non-onsite $U(1)^f$ symmetry, providing an analogue of fractional quantum Hall response in an invertible phase. This non-onsite $U(1)^f$ symmetry again forbids Chern insulators carrying $c_-\in\mathbb{Z}$, while being compatible with invertible states with $c_-\in\mathbb{Z}+1/2$. This result motivates a systematic study of new classes of invertible phases and spin liquids enriched by non-onsite symmetries.

This paper investigates Lagrangians with arbitrary dependence on the Riemann tensor and any number of derivatives. Noether's second theorem is applied separately to ${\cal L}_{G}$ and ${\cal L}_{M}$, where the matter Lagrangian depends on a scalar field. For ${\cal L}_{G}$ diffeomorphism invariance requires that the generalized Einstein tensor satisfy $\nabla_{\alpha}E^{\alpha\beta}=0$ and that there is a current satisfying $0=\partial_{\alpha}(\sqrt{g}\, J^{\alpha}_{G2})$. The main result is an explicit formula for the superpotential $\Phi^{[\alpha\mu]}$ that solves $\partial_{\mu}\Phi^{[\alpha\mu]}=\sqrt{g}\,J^{\alpha}_{G2}$. Some applications to $f(R)$ gravity and various quadratic gravity theories are discussed. There are analogous results, including superpotentials, for the matter sector whenever the couplings to the matter fields contain derivatives of the metric.

We explore a fermionic dark matter (DM) extension of the Standard Model Effective Field Theory (SMEFT) and establish a complete renormalisation-group framework for its phenomenological investigation. We derive the anomalous-dimension matrix of all relevant dimension-five and dimension-six operators involving Standard Model (SM) and DM fields, enabling the consistent evolution of the associated Wilson coefficients (WCs) across energy scales. By combining renormalisation-group running with matching at the relevant thresholds, we construct a robust bridge between high-scale new physics and experimental observables. We then perform a comprehensive phenomenological analysis, evaluating the contributions of these operators to observables spanning a wide range of energies and deriving constraints on the WCs from current data. We obtain stringent and complementary bounds on the DM effective field theory (DMEFT) WCs from electroweak precision observables, flavour processes, lepton-flavour-violating decays, top-quark flavour-changing neutral-current decays, and invisible meson decays. Interpreted in terms of the effective scale of new physics, the resulting limits demonstrate that current precision measurements probe energy scales ranging from the TeV regime to several tens or even hundreds of TeV, highlighting the remarkable sensitivity of indirect searches to dark-sector interactions.

We formulate the theoretical aspects of direct waves (DWs) in the case of extreme-mass merger. A DW is a source-driven waveform characterized by a complex frequency $\omega_{\rm G}$, which reflects the orbital motion of the particle in the vicinity of the black hole, including a part of the orbit inside the ergoregion: its real part is governed by frame dragging and its imaginary part by the redshift of the source. Using the Green's function technique, we derive the source-driven frequency $\omega_{\rm G}$, describe its screening by the potential barrier, and discuss its relation to dynamically excited quasinormal modes (QNMs). We then introduce a pole-splitting method that divides the full waveform into a QNM-pole sector and a non-QNM sector. Unlike QNM filtering, which multiplies the waveform spectrum by a filter function and thereby deforms it through a frequency-dependent time shift (i.e., group delay), our pole-splitting method merely divides the transfer function into pole and non-pole parts, separating the full waveform. Simulating a quasi-circular plunge into a Kerr black hole with medium and rapid spins, we find that the frequency and decay rate of the non-pole sector in the dominant mode, $\ell = m = 2$, evolve consistently with $\omega_{\rm G}$-or with its screened counterpart $\omega_{\rm screen}$-establishing the DW as a probe of the ergoregion and of the redshift effect around a black hole.

We show that the inference problem of constraining the parton distribution functions of the proton from deeply inelastic scattering data can be formulated as a linear tensor reconstruction inverse problem. This means that instead of fitting model parameters to the world data, a reconstructive approach to solve a system of coupled linear functional integral equations can be formulated. We leverage the mathematical structures of the integral equations defined by perturbative QCD and global analysis to pose the problem of global analysis as a coupled system of linear integral equations, and construct a proof-of-principle methodology to solve it. To formulate this approach concretely, we review all next-to-leading order accuracy results for inclusive virtual photon, neutral current, charged current, heavy flavor production, and neutrino deep-inelastic lepton–proton scattering. This mathematical methodology of inference opens a path towards a model-bias-free extraction of the proton PDFs from the world data of deeply inelastic scattering in the spirit of indirect measurement employed in mathematical inverse problems, including robust estimation of uncertainties with reduced bias from model parametrization, while closely adhering to the established paradigm of perturbative QCD and global analysis.

We investigate non-invertible selection rules originating from the discrete $H$-gauging of theories with an underlying discrete global symmetry group $G$. To systematically describe these theories, we formulate a general framework for $H$-gauged models that incorporates generalized field transformations. Our approach naturally accommodates non-Abelian groups, for which multidimensional irreducible representations play an essential role. In such models with non-Abelian groups, the transformations induced by $H$ non-trivially mix the internal components of $G$-multiplets, potentially projecting out specific degrees of freedom. Consequently, conventional selection rules based on standard tensor product decompositions or conjugacy classes become insufficient. By analyzing the full semidirect product $G \rtimes H$, we introduce projected characters to derive necessary and sufficient conditions for non-vanishing $n$-point bare couplings. Furthermore, we demonstrate that the remaining field components obey an associative fusion-like algebra governed by their Clebsch-Gordan coefficients. Phenomenologically, these selection rules restrict allowed interactions and impose specific relations among coupling constants. We illustrate our results through concrete examples, including $\Delta(54) \cong \Delta(27)\rtimes \mathbb{Z}_2$ and $S_4 \cong A_4 \rtimes \mathbb{Z}_2$.

We construct canonical chiral $\mathcal N=(0,1)$ sigma models on Spin(7) manifolds. The Spin(7) structure fixes the rank-seven bundle of the left-moving fermions, whose quadratic index matches the tangent representation, so the internal anomalies cancel while the rank difference leaves the gravitational anomaly of one right-moving Majorana–Weyl fermion. A transverse section of the left-moving bundle has a 1D zero locus with induced String structure, and we compute its class in the first torsion group of topological modular forms. The class is nonzero precisely when the Euler characteristic of the target is odd. The standard Joyce action on the torus has no internal finite-group anomaly and can be gauged to define an exact chiral spin QFT. We show that the orbifold Euler characteristic is even throughout the diagonal Joyce family generated by coordinate reflections and half-shifts preserving the Cayley form. By contrast, a free antiholomorphic quotient of the Fermat sextic is a compact torsion-free Spin(7) target with Euler characteristic 1305 and realizes the nonzero class.

We prove the Chen–Yang volume conjecture for all sufficiently long integral Dehn fillings of any fixed marked fundamental shadow-link exterior. For each fixed filling, the exponential growth of its $SO(3)$ Turaev–Viro invariants recovers its hyperbolic volume along the full sequence of odd levels. The filling coefficients may have mixed signs and unrelated magnitudes. We also establish a complete asymptotic expansion of the signed $SO(3)$ Witten–Reshetikhin–Turaev invariant and identify the absolute leading coefficient explicitly in terms of adjoint Reidemeister torsion. Fixed even colors on the filling cores recover characters of the geometric holonomy. The key difficulty is cancellation in the signed surgery sum. Our main analytic tool transfers an exact reflection symmetry from a continuous model to the finite quantum sums. We control the error below the exponential scale of the surviving contribution. We also apply the method to a one-edge state sum restricted to central colors. The dominant contributions cancel, and for each sufficiently large fixed number of blocks we determine the smaller surviving exponential rate and its nonzero leading coefficient.

In bottom-up holographic QCD (HQCD), two primary approaches are commonly employed: the potential reconstruction method, where the background geometry is fixed a priori and the dilaton potential is derived, and the direct method, where the potential is specified explicitly. While the reconstruction method is highly effective for capturing the phenomenological properties of QCD under extreme conditions, a subtlety arises in that the reconstructed potential depends on the chosen holographic boundary conditions. To address this issue, we propose constructing a dilaton potential designed to reproduce the typical features of HQCD phase transitions obtained by the reconstruction method, rather than one derived solely from HQCD vacuum solution. Using a light-quark model as an example, we construct a potential that captures the principal features of the phase structure of this model. Its parameters are determined at zero chemical potential by minimizing the deviation between the temperature dependence on the horizon position in the direct and reconstructed models and by fitting to the same position of a critical endpoint (CEP). The resulting minimal-potential model satisfactorily recovers the physics of the light-quark model even at relatively small chemical potential. Specifically, it yields a first-order phase transition (FOPT) line close to those obtained from the reconstruction method. Additionally, the minimal-potential model reproduces a rising Cornell-like quark-antiquark potential up to the hadronic distance $\ell=1.5$ fm, which we use as a phenomenological finite-distance criterion for confinement. The location of the confinement/deconfinement crossover in this minimal-potential model is also close to its counterpart in the original light-quark model.

Logarithmic supertranslations have been shown recently to be symmetries of the gravitational field at spatial infinity. We extend this work by proving explicitly that they are also symmetries at null infinity. We also show that the logarithmic supertranslation charges match at the “corner" where spatial infinity and null infinity meet. This fully establishes that the asymptotic symmetry group of gravity in the asymptotically flat context contains the logarithmic supertranslations.

We develop a systematic correspondence between massless contact amplitudes in an unbroken theory and massive contact amplitudes after spontaneous symmetry breaking. Our construction employs the spin-transversality (ST) massive amplitude basis, with the systematic high energy expansion through minimal-helicity-chirality (MHC) amplitudes. The resulting $U(2)=SU(2)\times U(1)_t$ description of a massive particle makes the semi-standard Young-tableau construction of massless Lorentz structures directly applicable to massive amplitudes. When the leading-order MHC component has a massless contact limit, it is one-to-one matched directly to its UV amplitude. Otherwise, five exceptional classes of ST amplitudes are identified, their first non-zero descendant components are matched through conserved current couplings to the massless contact amplitude. We apply the framework to the one-flavor electroweak sector of the Standard Model Effective Field Theory (SMEFT) through dimension eight, obtaining explicit relations between unbroken-phase Wilson coefficients and broken-phase ST amplitude coefficients for amplitudes with three to eight external particles.

Naive estimates based on Einstein gravity with Lagrangian $\frac{1}{2}M_{pl}^{2}(R-2\Lambda)$ suggest that, if the radiation era extended back to the Big Bang (i.e., as far back as the classical spacetime background makes sense), this would result in an over-production of dark matter and a relic cosmic background of thermal gravitons. Here we revisit these conclusions in quadratic gravity, the minimal renormalizable completion of Einstein gravity, whose Lagrangian also includes the terms $\frac{1}{6}f_0^{-2}R^2-\frac{1}{2}f_{2}^{-2}C^{2}$. Assuming the radiation era does extend back to the bang, we find a novel relation between the coefficient $f_{2}$ and the dark matter mass $m_{dm}$, needed to obtain the correct dark matter abundance. This yields a new gravitational production mechanism for dark matter (e.g., stable right-handed neutrinos). Moreover, the presence or absence of the relic graviton background (detectable by forthcoming CMB experiments via its small imprint on $N_{{\rm eff}}$) will place new constraints on $f_{0}, f_{2}$.

Quantum field theory on curved and non-inertial backgrounds contains background- and foliation-dependent quantities in the canonical Lagrangian, the hypersurface inner product and bilinear form, as well as in the equal-time anti-commutation relations. In this work, we determine a local fermion-field redefinition that brings these canonical structures into their standard-Minkowski forms, i. e., the forms they assume in Cartesian inertial coordinates on Minkowski spacetime, where the zeroth world coordinate is identified as the coordinate of time. Starting from the generally covariant Dirac action minimally coupled to a spin-1 gauge field, we derive the corresponding Lagrangian, fermionic inner product, and quantization rule in an Arnowitt-Deser-Misner decomposition, formulated in arbitrary world coordinates. We identify the generalized temporal gamma matrix as the common geometric factor governing the canonical temporal structure of all three quantities. Using a field redefinition, we transform this generalized temporal gamma matrix to its standard-Minkowski form, thereby mapping the fermionic inner product and the equal-time anti-commutation relation to their standard-Minkowski expressions, while transferring the explicit background and foliation dependence to the transformed Lagrangian and fermion-field operators. We show that such a field redefinition necessarily consists of a local rescaling and a fixing of the local Lorentz frame. This procedure restores the conventional canonical normalization from standard-Minkowski spacetime used for fermionic mode quantization and occupation-number operators. The transformed Lagrangian consequently assumes a generalized first-order Schrödinger form, leading to the familiar rest-energy term and spacetime-magnetic couplings, as well as to the leading non-relativistic limit, in which temporal derivatives are separated from spatial ones.

Fuzzy-sphere regularization gives numerical access to three-dimensional conformal field theories (CFTs), but locating one requires testing for criticality across the parameter space of microscopic couplings. We reduce the search cost by about two orders of magnitude, combining an exact diagonalization based on states having definite total angular momentum with a certified reduced-basis emulator that reconstructs energies, observables and their derivatives continuously across the couplings from a handful of exact solutions per system size. The combination reproduces the published ground-state-energy analysis of the fuzzy-sphere Ising model and the published conformal data of a three-flavor fuzzy-sphere realization of the O(2) Wilson–Fisher CFT, including quantities defined by parameter derivatives. Applied to the O(2) model with no CFT input, the ground-state-energy criterion locates the critical coupling to within half a percent of a density matrix renormalization group value obtained on systems more than twice the size, and maps the critical line of the model across the coupling plane. Ground-state criteria locate the critical line robustly, but the point they select along it is weakly determined, and the computed dimensions come closest to the bootstrap elsewhere along the line.

We develop an effective description of a two-dimensional cosmological end-of-the-world brane embedded in AdS$_3$, with a scalar field localized on the brane. Integrating out bulk degrees of freedom, especially in the small-gradient regime, the effective action reduces to a Liouville-like theory coupled to the brane scalar. We then construct brane trajectories whose induced geometry realizes slow-roll inflation and reconstruct the associated scalar profile and potential. We also study regular Euclidean brane geometries that admit a smooth continuation to Lorentzian de Sitter and inflationary universes, and evaluate the semiclassical on-shell action for the de Sitter solution. Finally, we analyze linearized inhomogeneous perturbations and find no exponentially growing mode within the regime of validity of the approximation.

We discuss a new family of publicly available collinear fragmentation functions (FFs) for pseudoscalar quarkonia, the NRFF1.0 set. It builds upon the Heavy-Flavor Non-Relativistic evolution (HF-NRevo) scheme, designed to describe heavy-hadron formation through leading-power fragmentation at moderate and large transverse momentum. Heavy-quarkonium production naturally involves both perturbative and non-perturbative QCD dynamics, from the production of the heavy $Q\bar{Q}$ pair to its formation into a physical bound state. Within NRFF1.0, Non-Relativistic Quantum Chromodynamics (NRQCD) provides the theoretical framework for calculating the FF inputs at the initial scale, which are subsequently evolved through the HF-NRevo scheme. This setup provides a precision baseline for investigating the underlying partonic hierarchy and jet structure across the moderate- to high-transverse-momentum regime. The explicit treatment of partonic channels and heavy-flavor thresholds makes this framework particularly suitable for exploring quarkonium-in-jet fragmentation, jet-quenching sensitivity, energy-loss mechanisms, and the emergence of medium-modified fragmentation patterns in the quark-gluon plasma.

We construct and study possible astrophysical signatures of the rotating counterparts of two charged regular black holes, namely the Ayón–Beato–García (ABG) and Balart–Panotopoulos–Rincón (BPR) spacetimes – obtained using the Newman-Janis algorithm. After verifying the regularity of the rotating metrics, we study massless scalar perturbations, compute the quasinormal mode (QNM) spectra, and characterise their dependence on the spin and charge parameters. Grey-body factors (GBFs) are computed, and the QNM-GBF correspondence is verified. The low-frequency superradiant amplification factor is also examined via matched asymptotic expansions. The Lyapunov exponents are used to connect the eikonal QNM damping rate to photon-orbit instability. Additionally, from shadow profiles, we constrain the parameter space of rotating regular black holes using the Event Horizon Telescope (EHT) observations. Across all the probes, we find that the rotating BPR and Kerr–Newman black holes behave almost indistinguishably from one another, while the rotating ABG geometry exhibits distinct perturbative, scattering, and geometric properties, particularly at larger values of spin and charge. Our analysis indicates that differentiating between charged rotating regular black hole models may be possible using gravitational wave and shadow observations.

The recent observation of a 220 PeV neutrino event (KM3-230213A) by the KM3NeT observatory presents a formidable challenge to standard astrophysical source models. We investigate the hypothesis that this ultra-high-energy signature originates from the terminal evaporation burst of a Primordial Black Hole (PBH). Since PBH evolution spans cosmic history, static vacuum approximations fail to capture early-universe dynamics. Embedding the PBH in a cosmological background via the McVittie spacetime, we demonstrate that early-universe cosmological accretion and expansion-suppressed Hawking emission shift the required initial mass window for a terminal burst occurring today. We show that although the early universe environment dictates the black hole's overall lifespan, its final explosion today ($z \approx 0$) is governed by standard Schwarzschild thermodynamics. This mechanism naturally produces the intense 220 PeV local flux while suppressing early emissions, thereby satisfying diffuse isotropic background limits. Consequently, this dynamical framework alters the mapping between current ultra-high-energy neutrino observables and the primordial curvature perturbations that seeded them.

We consider Yang-Mills theory with two infinite parallel plates, separated by a distance \(L\), that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new \(L\)-dependencies into the GZ gap equation. This would make the Gribov mass \(\gamma\) dynamically dependent on \(L\), implying an interesting interplay with the Casimir energy. However, we show that no such dynamical \(L\)-dependence occurs within the current approximation.