Papers

We study a kinematical consequence of the Hopf-algebraic momentum composition law in $\kappa$-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues $P_\mu$ are nonlinearly related to the ordered-plane-wave labels $p_\mu$. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity $P_+\equiv P_0+P_4=\kappa e^{p_0/\kappa}$ enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent $\kappa$-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by $P_\mu$ can be expanded into distinct auxiliary branches. If $P_\mu$ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables $p_\mu$ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

We regularize the Aichelburg-Sexl shock-wave geometry for massless particles by smearing the point-like source over a string-inspired length scale $l_0$. A radial extension of the transverse geometry admits a zero-throat Einstein-Rosen interpretation. For a photon wave packet of longitudinal extent $L$, the regularized gravitational self-energy of a transversely separated pair is $E_{\rm GSE}\sim \frac{4G(\hbar\omega)^2}{c^4L} \ln\!\left(\frac{d^2}{l_0^2}\right)$, where $d$ is the transverse separation. The factor $1/L$ strongly suppresses the interaction, giving gravitational stability times greater than $10^{30}$ years for optical photons. We also examine an effective two-dimensional entanglement-entropy description of the shock-wave geometry. The entropy construction reproduces the same dependence on the scales $d$, $L$, and $l_0$, and can be calibrated to reproduce the normalization of the direct self-energy calculation. However, we find that the gravitationally induced excess entropy, and hence the self-energy inferred from this prescription, is the same for Bell-entangled and unentangled photon pairs having identical energy-momentum distributions. This agrees with the direct geometrical calculation, since the classical two-shock metric depends on the stress-energy tensor but not on the polarization entanglement. The present construction should therefore be understood as a semiclassical ER-like geometry motivated by ER=EPR, rather than as a complete realization of the conjecture. A geometry whose connectivity tracks the amount of quantum entanglement would require a quantum-gravitational description sensitive to state-dependent correlations beyond the one-point stress-energy tensor.

We investigate Kerr-Schild-AdS geometries in quadratic f(R) gravity without imposing the constant-curvature condition R=R_0 a priori. We show that the field equations dynamically enforce constant scalar curvature and uniquely select the Kerr–AdS family of solutions. Thus, quadratic f(R) gravity admits no Kerr–AdS solutions beyond the Einstein branch, establishing a no-go theorem for this class of geometries.

We investigate Nielsen's geometric approach to quantum complexity in the presence of multiple cost factors, extending the standard framework where a single penalty distinguishes easy from hard directions of the group manifold. By introducing a hierarchy of penalties associated with different degrees of non-locality, we develop a generalized right-invariant complexity geometry and analyze its implications for geodesic evolution. We derive the modified Euler-Arnold and Jacobi equations and study how multiple cost factors reshape the structure and scaling of conjugate points, where geodesic optimality breaks down. The formalism is illustrated in two settings: a single-qubit system with two cost factors, where we develop a semi-analytic approach to investigate complexity growth and its dependence on penalty hierarchies, and SYK-type models, where we analyze both free and chaotic regimes. In these many-body systems, we show that distinct non-local sectors generate multiple families of conjugate points whose occurrence depends on both the cost hierarchy and the system size. Our results highlight how refining the penalty structure provides a richer and more realistic description of quantum complexity and its dynamical behavior.

In this work we discuss in detail a global analytic expansion scheme for the solutions of the `t~Hooft-Polyakov monopole profile equations for arbitrary $\lambda/e^2>0$ based on the findings presented in a recent resurgence-oriented letter arXiv:2602.14620 [hep-th], which the present study significantly expands upon. A uniformly convergent functional perturbation series developed around universal, surprisingly simple, analytic non-perturbative background profiles corresponding to a partial resummation of the Borel-plane expansions suggested there, is constructed; a perfect match to what is known about the full solutions' local behaviour at zero and infinite radii is achieved, along with simple analytic prescriptions for the locally inaccessible numerical parameters therein.

We introduce IterInt, a novel package implemented in both Mathematica and C++ for the numerical evaluation of iterated integrals involving arbitrary integration kernels. After the user has defined the integration kernels, IterInt transforms the iterated integrals into a system of first-order linear differential equations which can be solved efficiently and with high precision using well established libraries. IterInt is also able to automatically perform shuffle-regularisation. This makes it possible to evaluate also integrals where the integrand has a pole at the starting point of the integration path. As an illustration of our code, and also to validate it and gauge its performance, we compare the output of IterInt to the results obtained by GiNaC for ordinary and elliptic multiple polylogarithms, and also to existing results for the first few orders for banana integrals with up to four loops.

We compute the commutator of a scalar field minimally coupled to gravity at leading order in $G_N$. The commutator is operator-valued, with terms involving derivatives of Dirac deltas supported on the Minkowski light cone. When evaluated on classical/coherent graviton states, these terms “bend" the support of the commutator in precisely the way required to recover standard causality on a classical curved spacetime. However, these terms are also associated with a variance and are thus a source of uncertainty in the causal relations between events. We quantify this effect for a thermal state of gravitons at temperature $T$. In the large-time limit, the uncertainty of the lightcone position is given by $$ \text{Var}(\delta x) =\frac{4G_NTt}{3}\, , $$ where $\delta x$ is the displacement from the classical lightcone at $|\vec x| = t$. We obtain this result by subtracting a universal vacuum contribution that is logarithmically UV divergent and subleading at late times.

We present a four-dimensional deconstruction of the extra-dimensional axion arising from a $U(1)$ gauge theory in a five-dimensional orbifold, where the axion is identified with the Wilson line of the $U(1)$ gauge field and its coupling to QCD is generated by a 5D Chern-Simons (CS) term. We construct the corresponding 4D moose (quiver) gauge theory with link scalar fields, in which the axion emerges as a collective pseudo-Nambu-Goldstone boson. The axion-gluon coupling is described by a gauged Wess-Zumino-Witten term, providing the 4D counterpart of the 5D CS term. We further analyze non-perturbative effects from zero-mode and “fractional” instanton configurations. While the latter is exponentially suppressed in the regime corresponding to the 5D description, ensuring consistency with the higher-dimensional picture, we point out that this suppression can break down for smaller instantons whose inverse size exceeds the 5D cutoff scale, leading to a potentially significant effect. We also study axion potentials induced by bulk matter fields and boundary-localized symmetry-breaking operators, reproducing the characteristic nonlocal suppression associated with propagation in the extra dimension. Our construction provides a renormalizable 4D framework with a transparent understanding of the axion shift symmetry and its quality.

We investigate the relation between gravitational dynamics and the second law of thermodynamics in a non-equilibrium framework. Extending Jacobson's thermodynamic derivation of the Einstein equations, we introduce a stochastic geometric flow for the spacetime metric and define entropy production as the ratio between forward and time-reversed trajectories. We show that entropy production is governed by curvature and matter contributions, and that its vanishing selects configurations satisfying the Einstein field equations. Classical general relativity thus emerges as the reversible limit of an underlying stochastic geometro-dynamics, while the second law arises from its non-equilibrium evolution.

We introduce three-dimensional asymptotically-FLRW spacetimes as a simplified setting in which to study asymptotic symmetries and radiation in cosmology. Their asymptotic symmetry group is $\text{BMS}_3^k$, a one-parameter deformation of $\text{BMS}_3$ controlled by the matter equation of state with parameter $k$, in line with the four-dimensional construction of Bonga and Prabhu. We analyze in detail the case of a scalar field matter source, which allows us to fully characterize the solution space and the boundary charges. In particular, we point out that the proper identification of the Bondi mass and angular momentum aspects in the metric requires a careful analysis which had not been laid out so far, even in the existing four-dimensional literature. When superrotations are present, the model exhibits subtleties similar to those appearing when dealing with ”generalized BMS” asymptotic symmetries in the four-dimensional case, and this requires a covariant definition of the news. We identify covariant notions of news, as well as of mass and angular momentum aspects by studying the vacuum structure, namely the orbits of the vacuum solution under finite $\text{BMS}_3^k$ transformations, and study the Wald-Zoupas prescription for the charges. We also show that these covariant aspects naturally appear in the Cotton scalars, which are the three-dimensional analogues of the Weyl scalars. Finally, we use these quantities to provide a first example of exactly conserved non-linear Newman-Penrose charges in three-dimensional gravity.

Quantum transit times have a long history of inequivalent definitions, including phase times, dwell times, and quantum-clock constructions. In this context we revisit the Salecker–Wigner–Peres stationary quantum clock as a phase-sensitive scattering observable, with clock time defined by the energy derivative of the transmission phase shift across the interaction region. For real compactly supported one-dimensional potentials, we show that the raw stationary Peres clock generically contains a universal \(1/\sqrt{E}\) continuum-edge term whose coefficient is fixed by low-energy scattering data. For the attractive square well, this threshold singularity is inherited from the vanishing exterior momentum and the associated scattering matching, rather than from resonant delay itself. We derive the exact stationary clock time for the square well and introduce a new threshold-subtracted clock observable. Away from exceptional zero-energy tuning, the subtraction removes the universal low-energy term and isolates the resonant contribution. Comparison with the dwell time and the transmission Wigner phase delay shows that the threshold-subtracted clock acquires the expected local Lorentzian form near isolated transmission resonances. Near the continuum edge, if \(\varepsilon\) denotes the detuning from threshold, the resonant peak grows only as \(\varepsilon^{-1/2}\), whereas the unsubtracted threshold background grows as \(\varepsilon^{-3/2}\). A symmetric barrier–well–barrier cavity and a numerical asymmetric two-step attractive well provide complementary controls. The result is a new threshold-subtracted stationary-clock candidate that separates universal threshold kinematics from pole-sensitive resonant delay.

We investigate whether the absence of experimental signals for supersymmetry and extra dimensions can be understood as a correlated phenomenon. Assuming the Gravitino Conjecture, we study the relation between the gravitino mass and the Kaluza-Klein scale in four-dimensional $\mathcal{N}=1$ supergravity from Type II compactifications with large extra dimensions. We parametrize the scaling of the full internal volume with respect to that of a large $p$-cycle through an anisotropy exponent $\alpha$, and derive the corresponding volume contributions to the Kähler potential. This leads to constraints on the scaling exponent $n$, linking the gravitino mass to the KK scale, and on the effective number $\alpha p$ of large dimensions. We find that the linear relation $n=1$ is compatible only with one or two large extra dimensions, precisely the cases that can still be probed at micron distances. In such scenarios, micron-sized extra dimensions imply a light gravitino and gauge-mediated supersymmetry breaking, whereas gravity mediation corresponds to compactification scales beyond current experimental reach.

It is known that the saddle describing the contribution of supersymmetric black holes to the index of four-dimensional superconformal field theories is degenerate. This degeneracy is a consequence of the one-form symmetry of the theory, and can also be seen as a specific logarithmic correction to the saddle-point action. We discuss the gravitational realization of the one-form symmetry and of the index saddle degeneracy in different holographic setups. In order to illustrate the spontaneous breaking of the one-form symmetry at infinite volume, we employ a gravitational realization of the Cardy-like limit of small chemical potentials where the black hole decompactifies into a black brane.

We formulate a systematic on-shell construction of perturbative amplitudes by combining the Feynman-tree theorem with BCFW recursion. Amplitudes are built entirely from on-shell tree amplitudes generated by BCFW and are supplemented by additional unobservable state-conjugate on-shell pairs, called vacuum pairs, whose momenta are integrated over Lorentz-invariant phase space. At fixed coupling order, the contributing tree amplitudes are classified by polygon bookkeeping, while their products form forests whose relative signs are fixed by inclusion-exclusion. We show that these signs coincide with the signs assigned by the full Feynman-tree-theorem cut expansion, so that the construction reproduces the ordinary perturbative loop expansion order by order. The dynamical tree input consists of the allowed three-point on-shell amplitudes; the particle spectrum, couplings, and color data are taken as given, and no off-shell object is introduced at any stage. As a nontrivial test of this equivalence, we study the four-gluon all-plus amplitude through orders $g^4$ and $g^6$. The on-shell construction reproduces the finite rational one-loop primitive amplitude and the known bare planar and non-planar two-loop primitive integrands, including the bow-tie terms in the planar primitive.

We study quintessence in $\alpha$-attractor models in light of recent DESI indications for dynamical dark energy. We show that the knee of the attractor potential provides an excellent approximation to the axion-like quintessence model used as a DESI benchmark. This leads to a simple relation between the axion decay constant $f_a$ and the attractor parameter $\alpha$, allowing the experimental constraints to be translated into a preference for $\alpha=\mathcal{O}(1)$, in agreement with string-motivated expectations. We solve the background dynamics numerically and find good agreement with the DESI-preferred evolution of $w(z)$ up to $z\sim\mathcal{O}(1)$. More generally, we point out that the agreement between axion-like and attractor potentials reflects a common requirement imposed by the data: today's potential energy and slope are both of order the Hubble scale in Planck units. We finally comment on the origin of the required initial conditions, which can naturally arise in multifield attractor scenarios.

We study the stochastic dynamics of heavy quarks propagating through the strongly coupled plasma of $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory at nonzero temperature in terms of the corresponding Kolmogorov equation, which correctly describes their kinetic equilibration and the non-Gaussian fluctuations in their momenta without having to restrict their velocity to the non-relativistic regime. Leveraging the heavy quark limit, we show that the evolution of the momentum space distribution function can be reformulated as a Hamilton-Jacobi problem, and therefore can be solved in terms of first-order ordinary differential equations. We solve these evolution equations in an infinite thermal plasma with a constant temperature for initial conditions specified by spherically symmetric heavy quark momentum distributions with a phenomenologically motivated shape that is steeply falling at large momentum. To highlight the distinctive features of the kinetic equilibration process, we compare their solutions with Fokker-Planck dynamics with the same drag coefficient and fluctuations chosen by hand to guarantee equilibration. We find qualitatively similar dynamics at small momentum, and very different dynamics at large momentum, where, much like in jet quenching phenomena, the steepness of the momentum distribution gives a larger relevance to unlikely events in which a heavy quark loses little momentum in a given time step. Such events are much less unlikely in the Kolmogorov evolution than in Fokker-Planck evolution with the same mean energy loss, meaning that equilibration at large momentum is significantly delayed. Our results provide a systematic description of heavy quarks propagating through strongly coupled plasma from the ultra-relativistic to the non-relativistic regime and point the way towards implementation in phenomenological studies.

Metastable cosmic strings provide a cosmological interpretation of the nanohertz stochastic gravitational wave background reported by Pulsar Timing Array (PTA) experiments. We revisit this scenario in a minimal dark-sector gauge theory, in which a complex Higgs doublet breaks $\mathrm{SU}(2)\times\mathrm{U}(1)\to\mathrm{U}(1)_{\rm IR}$ at a single symmetry-breaking scale. This one-scale setup predicts metastable $Z$-strings whose endpoints are monopole-like defects, and whose zero-temperature decay rate is controlled by the gauge couplings and mass ratios. We show that, once the string-forming transition occurs in a thermal plasma, the dominant decay channel is not the zero-temperature monopole nucleation but thermally induced nucleation on the string worldsheet. We determine the nucleation temperature $T_{\rm nuc}$, which we \rev{adopt as the reference string-formation scale}, from the one-loop finite-temperature effective potential with daisy resummation, and use it to evaluate the worldsheet bounce action throughout the model parameter space. \rev{Requiring a PTA-compatible gravitational wave} signal selects a narrow region in the model parameter space, in the $(\sin^2\theta_w,\sqrt{\beta})$ plane, where $\theta_w$ is the dark-sector weak mixing angle and $\beta\equiv M_\Phi^2/M_{Z}^2$ is the squared Higgs-to-$Z$ mass ratio. Thermal effects modify the zero-temperature picture significantly, shifting the PTA-compatible region towards lower values of the dark fine-structure constant $\alpha'$ and larger values of the monopole-to-string-tension ratio $\kappa$.

We develop a new bootstrap strategy for cosmological correlators at loop level, which we call spectral dispersion. It is based on two conceptual observations that a correlator can be recovered from its on-shell data, also known as nonlocal signals, by analyticity up to local counterterms, and that the on-shell data for a loop process take the form of a discrete sum over quasinormal modes. Technically, our method combines the dS spectral decomposition with dispersion relations. Using this technique, we bootstrap new results in a simple and intuitive form for 3-point and 4-point correlators with 1-loop massive exchanges of scalar and vector bosons, either directly or derivatively coupled. Applications of this bootstrap technique to higher spins and higher-loop banana graphs with dS covariant dispersions but noncovariant couplings are also straightforward.

We study a dyonic black hole in a Lorentz-violating gravity that carries a background Kalb–Ramond field and is pierced by a cloud of strings. The resulting metric reduces to the recent Lin–Liu–Liu solution when the string density~$\xi$ is switched off, and to the Duan and Yang solutions in further degenerate limits. We work out the timelike circular geodesics and read off the quasi-periodic oscillation (QPO) frequencies $\nu_{\phi}$, $\nu_r$ and $\nu_\theta$ within both the relativistic-precession and epicyclic-resonance models. We then map these frequencies onto the observed twin-peak signals of XTE~J1550$-$564, GRO~J1655$-$40 and GRS~1915$+$105, and place constraints on $(\ell, \xi)$ from a Markov chain Monte Carlo (MCMC) fit. We extract the full thermodynamic dictionary, first law and Smarr relation included, and follow the heat capacity, free energy and sparsity of Hawking radiation through their dependence on the four parameters $(M, Q, p, \ell, \xi)$. Finally, we compute the spectral energy emission rate and look at the photon-sphere and shadow radii in the presence of the cosmic string. The Lorentz-violating coupling $\ell$, the magnetic charge $p$, and the string density $\xi$ all leave distinct fingerprints on the dynamical, thermodynamic and radiative observables, with $\xi$ exerting the strongest pull on the ISCO, the shadow size and the sparsity of Hawking emission

We present a reduced dimension theoretical framework for studying quantum field theories at finite density, providing a tractable model for investigating non-Fermi liquid (NFL) behavior near quantum phase transitions. Our approach departs from the standard paradigm by placing bosons and fermions in different spatial dimensions: bosonic fields reside in a $(d+1)$-dimensional bulk, while fermionic fields are confined on a $d$-dimensional boundary. This dimensional separation significantly simplifies the renormalization group (RG) analysis of gapless boson-fermion coupling. We demonstrate that the tree-level boson exchange contributions, which typically exhibit logarithmic divergences, become finite in our reduced-dimension scheme. Furthermore, the $\log^2$ and $\log^3$ divergences that characterize 1-loop four-fermion interactions in conventional treatments are reduced to logarithmic divergences within this framework, substantially improving the convergence properties of the perturbative expansion and allowing controlled theoretical analysis of NFL physics.

The spanning cuts method is a powerful approach to reduce the cost of IBP reduction while computing Feynman integrals. However, its usage is limited due to the so-called consistency problem. It was unclear why the IBP reduction coefficients can be inconsistent with each other between different cuts. In this paper, we report a mechanism behind this inconsistency. We found that the IBP relations can be violated under the cuts, if we blindly erase the hidden terms that are proportional to the “vanishing” Feynman prescription parameters in the relations. In some cases, the cut introduces pinch singularities, which cancel the vanishing Feynman prescription parameters, making the hidden terms finite. In various cases, the error comes from omitting such finite hidden terms. We also claimed that the pinch singularity under the cuts are related to some hidden relations between the propagators. In this paper, we provide an algorithm and its implementation to find the linear hidden relations.

Fluctuations of conserved charges are among the main proposed signatures of the quantum chromodynamics (QCD) critical point, but their interpretation requires a dynamical description of how fluctuation correlators evolve during the finite lifetime of the quark–gluon plasma (QGP) fireball. The standard baseline for this evolution is Fickian diffusion, in which the diffusive current follows the local density gradient instantaneously. This instantaneous-current limit can miss delayed-response effects when the current-relaxation time becomes comparable to the relaxation time of the relevant fluctuation modes. In this work we extend this baseline to Maxwell–Cattaneo diffusion, where the current relaxes on a finite time scale and therefore retains memory. We derive closed evolution equations for multi-point Wigner functions and convert the freezeout correlators into acceptance-dependent cumulants along representative trajectories in the QCD phase diagram. While Fickian diffusion already causes the correlators to lag behind their instantaneous equilibrium values, finite current relaxation introduces an additional memory effect beyond this diffusive lag. As a result, current memory can suppress, shift, and reshape the non-monotonic behavior of the cumulants relative to both instantaneous equilibrium and Fickian diffusion, with the most visible effects appearing in higher-order cumulants and their ratios.

Density cube theory extends the canonical quantum density matrix $\rho_{ij}$ with the addition of an extra index to $\rho_{ijk}$. The elements of the density cube with two different indices, $\rho_{iij}$ and $\rho_{ijj}$, correspond to the real and imaginary parts of the off-diagonal element $\rho_{ij}$ of the density matrix and describe double-path interference, while those with three different indices describe non-canonical triple-path interference. In this letter, we propose an equation of motion for the density cube, obtained from the quantization of ternary Nambu dynamics, and find that pairs of triple-path interferences oscillate into each other.

We present a new construction for black-bounce spacetimes based on a deformation of the scale function that acts as a geometric saturation rather than introducing a prescribed constant minimal length, as in conventional black-bounce models. This function encodes the gravitational information of the underlying vacuum counterpart, keeping the geometric quantities of the deformed metric finite in the short-distance region where tidal forces and curvature invariants of the vacuum geometry diverge. The deformation saturates at short scales, suppressing curvature divergences without requiring a potentially unstable de Sitter core. The resulting regular geometries with spherical, planar, and hyperbolic transverse sections describe regular black holes (RBHs), extremal RBHs, and traversable wormholes. A key result is that the deformed geometry remains finite at $l=0$ in all regimes, while, depending on the parameter space, the bounce, identified with the minimum of $R(l)$, may remain in the short-distance region or shift to a larger finite value of $l$. Thus, the deformation regularizes the central region and, in some regimes, also modifies the global spacetime profile. Spherical and planar RBHs satisfy the standard energy conditions near the bounce, showing that a geometric bounce does not necessarily require exotic matter sources in this region. In the hyperbolic case, the energy conditions depend more strongly on the mass parameter, being satisfied near the bounce for positive-mass RBHs but violated for negative-mass and extremal configurations. The hyperbolic sector also admits regular negative-mass black holes. For wormhole geometries, the WEC and NEC are violated near the throat, as expected.

Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters – viewed as the Wilson coefficients of hydrodynamic EFTs – both in continuum and on the lattice.

Possible violations of the equivalence principle are investigated within the framework of metric-affine gravity and their connection to finite-temperature effects are highlighted. Thermal corrections to particle dynamics, originally derived in a quantum-field-theory setting, can be evaluated in a purely Riemannian framework and lead to a shift in the gravitational-to-inertial mass ratio. We show that the ensuing departure from universality of free fall can be also formulated in metric-affine gravity, where the presence of the non-metricity tensor modifies the Newtonian law in a way that closely parallels the finite-temperature scenario. Furthermore, we introduce a generalized Fermi-Walker derivative adapted to non-Riemannian contexts, which naturally reveals that no orthonormal tetrad can be propagated along an observer worldline. Although metric-affine gravity admits a pointwise realization of the Einstein equivalence principle in its gauge-theoretic, elementary-matter form, the new operator offers a direct geometric signature that this principle, in its modern formulation, is not retained in general. Potential tests of the analyzed effects are also discussed.

We investigate a three-dimensional ghostly Hamiltonian realisation of the fully degenerate resonant sixth-order Pais-Uhlenbeck oscillator. On the classical level, the phase-space flow is non-diagonalisable and decomposes into two complex-conjugate Jordan chains of length three, explaining the appearance of oscillatory solutions with secular terms. Upon quantisation, we construct intertwining operators whose quadratic combinations generate a hidden spectrum-generating $\mathfrak{u}(2,1)$-algebra. The associated descendant spaces are finite-dimensional invariant subspaces carrying non-trivial Jordan structure. Although these spaces admit a natural decomposition into irreducible modules of a distinguished $\mathfrak{sl}_2$-subalgebra, this decomposition does not in general coincide with the Jordan decomposition of the Hamiltonian. We further derive a tri-Hamiltonian formulation from Lie point symmetries of the classical flow and show that the corresponding Hamiltonians are naturally encoded by the same hidden algebra. Nevertheless, unlike in the non-resonant case, no positive-definite linear combination of them generates the same dynamics. Finally, we analyse the common centraliser of the tri-Hamiltonian family in $U(\mathfrak u(2,1))$, showing that the natural higher-order candidate $Q$ is reducible and yields no independent classical or quantum integral. The model thus provides a resonant higher-derivative system in which hidden $\mathfrak{u}(2,1)$ symmetry, classical and quantum Jordan structures, and multi-Hamiltonian geometry coexist.

We calculate the azimuthal angular decorrelation of diffractive dijets in ultra-peripheral heavy-ion, $ep$, and $eA$ collisions to probe non-perturbative diffractive transverse momentum-dependent distributions. Focusing on the dominant semi-inclusive channel with an unobserved semi-hard gluon, we perform an all-order resummation of soft gluon emissions for the transverse energy-energy correlator observable, accounting for both initial and final state radiation. We also analyze heavy-quark pair production and demonstrate the sensitivity of the decorrelation to the jet axis definition. Finally, we provide numerical predictions for relevant kinematics at LHC UPCs, HERA, and the future EIC. Our results demonstrate that the acoplanarity of diffractive dijet production could serve as a promising probe of diffractive transverse momentum-dependent distributions.

Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-$q$ model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.

We study $O(2)$-equivariant spectral flow for Dirac operators on a finite warped cylinder equipped with fixed admissible regularized APS boundary conditions. The twisting bundle is a real higher-rank orthogonal bundle, and reflection symmetry is implemented by a fiber involution. After complexifying the twisting bundle and diagonalizing the orthogonal twist, the Dirac equation decomposes into a scalar Fourier-mode radial equation, with moving rotating blocks and stationary neutral blocks. After regrouping conjugate and reflection-paired blocks, the crossing contributions define real $RO(O(2))$-classes. Consequently, we obtain an explicit blockwise formula for the $RO(O(2))$-valued spectral flow of the resulting regularized APS family. Under the standard self-adjoint Fredholm, endpoint-invertibility, and regular-crossing hypotheses, together with a fixed neutral-sector convention, this formula is obtained by assembling the local crossing contributions of the separated blocks. It refines ordinary integer-valued spectral flow and shows explicitly how the dimension map $RO(O(2))\to\mathbb Z$ loses representation-theoretic information. We also discuss the rank-three case, including the role of the fixed neutral sector, and the corresponding endpoint $\eta$/APS index interpretation.