Papers

Pre-geometric Gravity investigates the non-metric features of spacetime near the Planck scale, from which the gravitational interaction arises as a low-energy effective theory via a mechanism of spontaneous symmetry breaking. With a view of amending the classical singularities found in black hole geometries, in this work we study pre-geometric black hole configurations with spherical symmetry, and present exact solutions for different pre-geometric theories in vacuum via the correspondence principle. These solutions are the pre-geometric analogue of the (anti-)de Sitter-Schwarzschild metric, from which such type of black hole geometry is thus expected to emerge. In one case, the pre-geometric solution also exhibits an (anti-)de Sitter core of Planckian size. The main result is supplemented with an analysis of the pre-geometric version of Birkhoff's theorem.

We study photon conversion into light particles, such as dilatons, axions, and gravitons, induced by background magnetic fields, and formulate the resulting evolution in terms of the Stokes parameters. We show that photon conversion reduces to an effective non-unitary evolution of the photon sector. In the perturbative regime, the Hermitian and anti-Hermitian parts of the effective photon Hamiltonian are related through Kramers–Kronig relations, revealing that the changes in the Stokes parameters are not independent. We apply this general framework to photon evolution in Gaussian stochastic magnetic fields with possible helicity, and derive the ensemble-averaged evolution of the Stokes parameters. We find that two nonzero contributions arise even in the absence of magnetic helicity, which respectively correspond to the overall attenuation of all the Stokes parameters and to an irrelevant overall phase. We also find that magnetic helicity gives rise to two additional contributions, one of which changes the circular polarization while the other induces a rotation of linear polarization. These contributions form two Kramers–Kronig pairs. In particular, photon conversion induced by magnetic helicity is accompanied by both circular-polarization and birefringent responses. The same structure appears in dilaton-photon, axion-photon, and graviton-photon systems, revealing universality of photon conversion in magnetic fields.

We investigate fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation. Serving as a comparison channel, the dipole coupling $p_1$ is found to produce a soft asymmetric reconstruction without opening a clean hard Mott gap. Our main analysis then focuses on two axion-dependent non-minimal couplings modulated by current mixing. The $p_2$ tensor channel suppresses the zero-energy Fermi peak and shifts the dominant spectral weight to finite frequencies, resulting in a flat-bottom reconstruction. In contrast, the $p_3$ vector channel creates a strong spectral asymmetry in momentum space, generating open, Fermi-arc-like segments. Varying the momentum-relaxation strength $\beta/\mu$ and the doping parameter $\chi$ reveals a channel-dependent response to the two-current background. Increasing $\beta/\mu$ generally broadens the $p_2$ response, whereas the one-sided $p_3$ feature varies non-monotonically under changes of the background parameters. These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations. These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations.

Different stages of cosmic evolution impose different requirements on the dark matter annihilation cross section. Sommerfeld enhancement provides a possible way to accommodate them. However, in the point-like dark matter scenario, satisfying these requirements with either $s$-wave or $p$-wave Sommerfeld enhancement can strongly constrain the dark matter and mediator masses and their coupling. A finite dark matter size introduces an additional parameter and may relax these constraints. Motivated by this possibility, in this work we study the $p$-wave Sommerfeld resonances of finite-size dark matter (like proton or neutron) without specifying its internal structure. We find that the $p$-wave contribution can exceed the $s$-wave contribution. Nevertheless, the finite-size $p$-wave resonances are weaker than those in the point-like case. Despite this suppression, their velocity dependence remains similar to that of point-like dark matter. We then extend our analysis to nugget dark matter composed of a small number of constituents. In this case, the $p$-wave Sommerfeld enhancement exhibits behavior similar to that of point-like dark matter.

The three gauge couplings of the Standard Model (SM) can be parameterized as the fine structure constant $\alpha$, the weak mixing angle $\sin^2\theta_w$, and the strong coupling $\alpha_s$. They are fundamental constants whose values remain unexplained. Previously we showed that minimizing magic production in charged-lepton scattering reproduces $\sin^2\theta_w$ with great precision. Here we study magic production in the six flavor-diagonal color-singlet channels $q\bar q\to q\bar q$ at tree level, including photon, gluon, $W/Z$, and Higgs exchange. Varying only $\alpha_s$, with all other inputs fixed at each center-of-mass energy, we find that the finite-$\alpha_s$ magic minimum in the top channel reproduces the $\overline{\mathrm{MS}}$ value of $\alpha_s$ to within $5\%$ from $1~$TeV to $10^9~$GeV. Higgs exchange involving the large top Yukawa coupling is essential for this agreement. All six channels produce near-minimal magic at the SM couplings, and reducing $\alpha_s$ toward $\alpha$ increases their magic production, potentially explaining why the strong interaction is “strong.” To understand why minimizing magic reproduces both $\sin^2\theta_w$ and $\alpha_s$, we conjecture that the parameters of fundamental interactions among color singlets reflect a principle of quantum computational efficiency, with the physical universe emerging from a quantum simulation subject to constrained resources.

I propose a Hamiltonian framework for chiral gauge theories (CGT) based on a Euclidean formulation which uses 2n dimensional chiral fermions on the boundary of a 2n+1 dimensional disk. In the original Euclidean formulation, boundary gauge fields were extended into the bulk using $2n + 1$ dimensional gauge field equations of motion (EOM) which creates a bottleneck for constructing a Hamiltonian. I present an alternate proposal for extending the gauge fields into the bulk that is compatible with both a Hamiltonian framework and a Euclidean path integral. Applying this to Abelian gauge fields produces exact expressions of interior fields as a functional of the boundary fields, which can be directly used in a Hamiltonian formulation. Euclidean analysis of the new gauge field extension shows that it can preserve the non-perturbative content of the original construction, including the behavior of topological charge, associated chiral fermion zero modes and an absence of the strong CP problem when applied to the Standard Model. This construction opens up a route to a Hamiltonian treatment and future quantum simulation of CGTs on a disk boundary.

In quantum mechanics of genus-1 potentials, perturbation theory around the topologically trivial saddle and non-perturbative instanton saddle are constructively related via the P/NP relation. Whether such a relation persists for higher-genus potentials has remained an open problem. In this work, we resolve it using tools from complex algebraic geometry combined with exact WKB. The classical energy conservation relation $p^2 = 2(E-V(q))$ defines a genus-g Riemann surface $X$, whose periods are naturally organized by its Jacobian variety $J(X) = \mathbb{C}^{\text{g}}/\Lambda$ via the Abel-Jacobi map, and independently by the solution basis of the associated Picard-Fuchs equations. We show that the physically relevant, WKB-active cycles are generally related to the Picard-Fuchs basis by a linear transformation that lies in $\text{SL}(2\text{g},\mathbb{Z})$ but not in the symplectic group $\text{Sp}(2\text{g},\mathbb{Z})$ once $\text{g}\geq2$, in contrast to the genus-1 case, where the two groups coincide. This mismatch is the obstruction that has made an explicit higher-genus P/NP relation elusive. We show that it can be resolved by passing to a modified Riemann bilinear identity, built from a suitably transformed intersection matrix, which the WKB-active periods do satisfy exactly. The result is an all-orders quantum P/NP relation valid for potentials of arbitrary genus, which we derive explicitly for genus-2 (quintic and sextic) and genus-3 (septic and octic) anharmonic oscillators.

Using the Mellin-Barnes representation of de Sitter propagators, we reduce tree-level heavy-particle exchange to finite integrals that converge at physical kinematics on mass-independent contours, and one-loop diagrams to the same integrand times a flat-space momentum factor. We evaluate the triple-exchange bispectrum without analytic continuation and compute the complete one-loop triangle at general mass. These give cosmological collider predictions, the oscillatory signatures of heavy particles during inflation, for multiple exchanges and loops at arbitrary masses.

We prove an exact identity, as convergent logarithmic germs at large Euclidean momentum, between the equal-mass two-dimensional $(n-1)$-loop sunset Feynman integral, with $n\geq4$, and the genus-zero one-point descendant invariants of the local Calabi–Yau $n$-fold $X_n=\operatorname{Tot}(K_{F_n})$, where $F_n\subset(\mathbb P^1)^{n}$ is a smooth $(1,\ldots,1)$ hypersurface. Writing $s$ for the momentum variable and $y=-1/s$, the identity reads \[ I^{(n-1)}_{\circleddash}(s)=(-1)^{n-1}yA\,\Bigl[nR^{n-1}-\theta_Q{\mathcal D}_0^\Delta\,R^{n-2} +\sum_{j=0}^{n-3}c_jR^j\Bigr], \] where $R=\log y+O(y)$ is the local mirror coordinate, $A=\theta_yR$, $Q=e^R$, ${\mathcal D}_0^\Delta(Q)$ is the primary one-point potential, and each $c_j$ has the form \[ c_j=c_j^{(0)}+\sum_{a=0}^{n-2}\bigl(c_{j,a}\,{\mathcal D}_a^\Delta(Q) +c'_{j,a}\,\theta_Q{\mathcal D}_a^\Delta(Q)\bigr) \] with the coefficients in $\mathbb Q[\zeta(3),\zeta(5),\ldots]$ the odd zeta values coming from the Gamma class. The descendant series ${\mathcal D}_a^\Delta(Q)$ are given explicitly by the ambient hypergeometric series and the inverse mirror map. We also prove global univalence of the principal mirror map, with explicit upper and lower bounds on the $Q$-Taylor radii, extract the full primary evaluation divisor and its integral cover transform, and reduce the ambient endpoint constants to a finite universal Gamma-class part and $\lfloor(n-1)/2\rfloor$ real parameters.

We determine the equal-mass two-dimensional three- and four-loop sunset Feynman integrals $I^{(3)}_\circleddash$ and $I^{(4)}_\circleddash$ at large Euclidean momentum in terms of the genus-zero Gromov–Witten theory of the local Calabi–Yau fourfold and fivefold $X_L=\operatorname{Tot}(K_{F_L})$, where $F_L\subset(\mathbb P^1)^{L+1}$, $L=3,4$, is a smooth hypersurface of multidegree $(1,\ldots,1)$. At two loops the sunset integral is governed by the prepotential of a local Calabi–Yau threefold. For $L\geq3$ the moduli spaces of unmarked stable maps have positive virtual dimension and there is no prepotential, therefore the Feynman integral is governed instead by the one-point potential $\mathcal F_{\gamma_L}$ with insertion $\gamma_L=H^{L-1}/(L-1)!$, by its gravitational descendants, and by $\zeta(3)$ boundary terms coming from the Gamma class. At both loop orders the coefficient of $R^{L-1}$ in the Frobenius expansion in the mirror coordinate $R$ is $-\theta_Q\mathcal F_{\gamma_L}$ with the Novikov variable $Q=\exp(R)$. At three loops the whole Feynman integral is an explicit expression in $\mathcal F_{\gamma_3}$ alone, because genus-zero recursion determines all descendant series from it; at four loops two diagonal series suffice, and the $\zeta(3)$ term is itself corrected by $\theta_Q\mathcal F_{\gamma_4}$. At three loops we also derive the analytic normalization independently, from the Picard–Fuchs equation and the polar part of a Mellin transform, prove integrality of the multiple-cover transforms for arbitrary integral insertions together with an explicit quantum-$K$ formula, and compute the exact period connection polynomials. Finally we give endpoint values along the Euclidean axis, bounds on the Taylor radii in the Novikov variable $Q$, a computer-assisted proof of the four-loop endpoint nonanalyticity, and a comparison of the normalizations at two, three and four loops.

Asymptotic Safety provides a promising framework for the quantization of Scalar-Tensor theories as non-perturbatively renormalizable quantum field theories. Over the past years, growing evidence has accumulated for the existence of non-trivial renormalization group fixed points in a variety of Scalar-Tensor models. In this work, we investigate the robustness of these fixed points under significant modifications of the computational setup. In particular, we employ a gauge condition that explicitly depends on the dynamical scalar field, going beyond a mere gauge-parameter deformation of the standard linear covariant gauges commonly used in the literature. Exploring different field parameterizations, we identify fixed points belonging to the Gaussian Matter class in four spacetime dimensions that are consistent with previous studies. The real part of the critical exponents associated with the scalar-field mass and the non-minimal scalar-curvature coupling turn out to have very small absolute value. We provide a comprehensive exploration of how the anomalous dimension of the scalar field and field parameterization impact those critical exponents showing that fixed-point candidates with two or four relevant directions emerge.

The island proposal guarantees a unitary Page curve for evaporating black holes, implying that operators deep behind the horizon must be fully reconstructable from asymptotic Hawking radiation. However, because the interior is causally disconnected and highly dynamical, standard entanglement wedge reconstruction methods, relying on global isometries or continuous modular flow, fail to provide this mapping. We resolve this by constructing a protocol for island reconstruction using the algebraic Petz map. By using modular theory, we reflect island operators into the accessible complement, transport them to the boundary, and map them into the radiation algebra. Furthermore, we demonstrate that this purely algebraic derivation naturally yields the structure of Papadodimas-Raju mirror operators. This framework provides a rigorous operational dictionary for the island formula, proving that information trapped inside a black hole can be decoded.

We develop a constructive framework for characterizing modulated symmetries and their gauging in $d$-dimensional lattice systems. The modulation profiles are organized as a finite-dimensional representation of the space group acting on a finite Abelian internal symmetry group. Since the corresponding automorphism group is finite, the nontrivial spatial action factors through a finite quotient of the space group, leading to periodic modulation patterns and providing a classification framework for discrete Abelian modulated symmetries. The symmetry-allowed local interactions are systematically obtained from a kernel construction, which also yields an algebra of open operators. Upon gauging, its elements are transmuted into extended Wilson and boundary operators while retaining their algebraic relations. In the deconfined regime, the resulting algebra realizes a mixed 't Hooft anomaly, providing a microscopic route to Abelian crystalline symmetry-enriched topological phases (SETs). These SETs do not mix electric and magnetic sectors, which transform in mutually contragredient representations, thereby preserving their braiding pairing. We illustrate the framework through explicit examples and show that several models present in the literature fit naturally within our construction.

We present a new derivation of the exact compact oscillon in the signum-Gordon model using Fourier methods. This approach decomposes the oscillon into an infinite, uniformly convergent series of discrete modes consisting of a fundamental frequency and its odd higher harmonics, in contrast to standard analytic potentials, where the corresponding infinite perturbative series fails to converge. Crucially, our oscillon evades the non-existence theorem for spatially localized, small-amplitude periodic states. We investigate the accuracy of truncating the Fourier series and find that the primary mode alone provides a remarkably accurate approximation of the exact solution, with agreement improving significantly when the first two non-vanishing harmonic modes are included. Furthermore, we generalize this framework to a swaying compact oscillon with a periodically moving boundary. We show that describing such an oscillon requires even-order modes, whose coupling with the odd source terms induces a dynamic modulation that generates the swaying motion, even though the spatial Fourier profiles themselves are time-independent.

We study gauge-invariant two-matrix polynomials of degree $L$, corresponding to the states in the $su(2)$ sector of $\mathcal{N}=4$ super Yang-Mills theory with gauge group $U(N)$ or $SU(N)$ at finite $N$. For the $U(N)$ theory, the state space has the structure of an algebra $\mathcal{A}_N(L)$, which is a direct sum of permutation centraliser algebras, i.e. sub-algebras of the group algebra $\mathbb{C}[S_L]$ of $S_L$. For $N \ge L$, $\mathcal{A}_N (L) = \mathcal{A} (L)$ is independent of $N$, and the one-loop dilatation operator acts on $\mathcal{A}(L)$ with $N$ as a parameter. For $N < L$, $\mathcal{A}_N (L)$ is a subspace of $\mathcal{A}(L)$ defined using a finite-$N$ cutoff on Young diagrams with $L$ boxes. We establish two results on the eigenspaces of the one-loop dilatation operator. Our first main result is that the characteristic polynomial of the one-loop dilatation operator on $\mathcal{A}_N(L)$ divides the characteristic polynomial from $\mathcal{A}(L)$, continued to $N < L$. Our second result is that each eigenstate of the one-loop dilatation operator in the $SU(N)$ theory generates an infinite tower of eigenstates in the $U(N)$ theory, through the multiplication of single-letter traces. These towers define an eigenspace factorisation of the $U(N)$ theory labelled by the number of such traces. Further, we conjecture that the space of $SU(N)$-invariant polynomials in two traceless matrices at finite $N$ is isomorphic to the intersection of $\mathcal{A}_N(L)$ with the subspace of $\mathbb{C}[S_L]$ spanned by derangements. This intersection conjecture is supported by dimension counting. Finally, we propose a one-loop dilatation operator on the intersection, thus providing a direct permutation framework for the $SU(N)$ spectral problem at finite $N$. The computed spectra based on the proposal agree with the prediction from the eigenspace factorisation in the $U(N)$ theory.

The energy-energy correlator (EEC) is one of a handful of collider observables that can be computed analytically to high orders. As an energy-weighted cross-section, it exposes features of quantum field theory that scattering amplitudes do not, and it can be compared directly to data. As with scattering amplitudes, the analytic expressions require special functions beyond polylogarithms. In Henn et al., the EEC was computed to next-to-next-to-leading order (NNLO) for $\mathcal{N}=4$ super Yang-Mills (SYM) theory, and the result is expressed in terms of both harmonic polylogarithms (HPLs) and one two-fold integral, which contains elliptic curves. In this work, we report a complete result including the remaining elliptic sector, which is closely related to the sunrise Feynman integrals. We find the $j$-invariants of the EEC and the sunrise agree identically under a Möbius map, and thus the elliptic sector in the EEC lives on the $\Gamma_1(6)$ modular curve of the sunrise integral. We then express the answer in terms of iterated Eisenstein integrals, which can be evaluated to high precision quickly. The analytic form also allows a first study of the EEC Landau bootstrap, and the understanding of its function space in $\mathcal{N}=4$ SYM offers a concrete handle on the elliptic sector of the EEC in QCD. Many of the technical results in this paper were completed with AI under human supervision.

Tree-level matrix elements sit at the heart of collider event generation, but their cost rises rapidly just where additional resolved radiation becomes most important. We present pyAmpliCol, a public generator aimed at extending the practical reach of colour-resolved matrix elements to higher multiplicities. It builds on the colour-ordered, off-shell-current strategy of AmpliCol, providing fast access to individual leading-colour flows while retaining the option of next-to-leading or exact full colour. The latter introduces its own high-multiplicity bottleneck: the dense interference of factorially many colour orderings. pyAmpliCol addresses this contraction with a fast Fourier transform on the symmetric group, preserving the exact colour result while avoiding the direct pairwise sum. Representative full-colour benchmarks demonstrate substantial speedups over the reference calculations considered here. It supports Standard Model processes and a broad class of UFO models, selected or summed helicities, vectorised evaluation and controllable numerical precision. It further provides colour- and spin-correlated Born quantities and tree-level colour connections at arbitrary perturbative order, opening the same framework to local subtraction and other higher-order applications. Together, these capabilities connect high-multiplicity matrix elements to their use in event generation, merging, parton showers and precision calculations within a single generator.

We study two-point functions of chiral primary operators in $\mathcal{N}=4$ Super Yang-Mills in the presence of a half-BPS surface defect. Such a defect preserves only the diagonal combination of transverse rotations and of a global U(1) R-symmetry, so that the correlator depends on one additional cross-ratio and splits into sectors of definite angular charge. We solve the superconformal Ward identities and construct the bulk and defect superconformal blocks in all sectors, including the charged ones, which have no analogue for defects preserving transverse rotations. The solution contains a holomorphic sector, which we fix non-perturbatively by mapping it to a chiral algebra correlator. We extend this map to defects breaking transverse rotations, where it requires a redefinition of the modes of the two-dimensional current algebra, and use it to fix the charged sectors as well. We then use the defect dispersion relation to reconstruct the full correlator of the dimension-two chiral primary at leading order at large N and strong coupling. In the charged sectors long multiplets are absent and the answer is conjecturally exact in both N and the coupling; expanding it at weak coupling, we find perfect agreement with known results. From these correlators we extract infinitely many new pieces of defect CFT data. Finally, we reproduce the strong-coupling answer by an independent Witten diagram bootstrap on the rotation-invariant locus.

We study the Carroll-Weyl gauged null string in the Poincaré patch of $\mathrm{AdS}_D$ and its BRST quantization. In Poincaré coordinates $X^A=(z,x^i)$, the radial conformal Killing vector $K=\partial_z$ becomes homothetic in a suitable conformally related frame. A field-dependent rescaling of the homothetic Hamiltonian constraint then leads to the radial-adapted basis $\mathcal{M}=\frac{1}{2}(P_z^2+P_iP^i)$, $\mathcal{L}=-P_AX'^A$, and $\mathcal{S}=P_z$, with $\mathcal{M}$ invariant along the Carroll-Weyl radial flow. Their modes form a $\mathrm{BMS}_3$ algebra extended by an abelian weight-one current. We classify the central extensions allowed by this residual algebra and find four independent cohomology classes in the $LL$, $LM$, $LS$, and $SS$ channels. We then construct the associated BRST complex, including the ghost pair for the radial Carroll-Weyl constraint. In the canonical highest-weight first-order representation, only the Virasoro-type central extension is realized: $(c_{LL},c_{LM},c_{LS},c_{SS})=(2D-54,0,0,0)$. Cancellation of the corresponding nontrivial BRST cocycle therefore gives $D=27$ in this representation. This differs structurally from the minimal flat Carroll-Weyl theory, where the dilation constraint $X\cdot P$ gives extra anomaly channels.

We introduce a systematic scheme for constructing the ODE/IM counterpart of generalised Gibbs ensembles, and apply it to the chiral sector of the Lee–Yang conformal field theory. We encode the chemical potentials in a deformation of the cubic oscillator, fixed order by order by requiring that the large-energy WKB period reproduces exactly the driving term of the corresponding thermodynamic Bethe ansatz equation; the subleading WKB periods then yield, as predictions, the deformed eigenvalues of the local conserved charges. We work out the spin-5 ensemble in detail for two states of the model: the ground state, in the module of the primary $\phi$, dual to the deformed cubic oscillator, and the primary of the identity module, dual to the same oscillator supplemented by an apparent singularity, a double pole whose position is fixed by a trivial-monodromy condition. In both cases, the Stokes multiplier obeys the Lee–Yang Y-system, and the deformed eigenvalues match, to the orders checked, an independent conformal-field-theory computation. The Borel resummation of the resulting series for the ground-state energy reproduces the numerical TBA solution over many orders of magnitude in the chemical potential. The scheme relies only on general features of the ODE/IM correspondence and applies to generalised Gibbs ensembles in other integrable models.

We show that the known six-point constraints on four-point amplitudes are sufficient for completion at arbitrary multiplicity in planar, four-dimensional maximally supersymmetric gauge theory. We construct massless tree amplitudes as formal series in the derivative expansion, with the standard supersymmetric Yang-Mills three-point amplitudes, unbroken R-symmetry, and parity invariance of amplitudes with only external scalars, holding the scalar labels fixed. For a positive leading four-point contact coefficient, the even coefficients in the logarithmic parameterization are fixed, while every real sequence of odd coefficients is realized by a completion at all derivative orders. The construction uses the field-theory Kawai-Lewellen-Tye bilinear and normalized matrices of sphere integrals. Exponentiating homogeneous components of their matrix logarithms varies the odd coefficients independently while preserving locality and factorization through the complete massless multiplet. The six-point conditions are therefore necessary and sufficient for such a completion. Higher-multiplicity consistency imposes no further restrictions on these four-point coefficients once the higher-point contact interactions are chosen consistently with the same symmetries and factorization conditions.

The tensor branch of six-dimensional $\mathcal N=(1,0)$ supergravity is characterized by a spectrum of BPS strings charged under the two-form gauge fields. Their charges span a cone in the tensor charge lattice, whose extremal rays are generated by primitive BPS string charges that become tensionless at the boundaries of the tensor moduli space. We develop a systematic procedure, based entirely on effective field theory data, to reconstruct the primitive BPS string generators and thereby determine the complete closed BPS string cone of any 6d $(1,0)$ supergravity theory. The key ingredients are the universal H-string, which allows us to isolate a fixed sector determined by classified LST blocks and gauge anomaly data from the remaining gauge-neutral E-string sector, and a BPS refinement of the Completeness Conjecture that ensures population of the relevant charge rays. We further show that this reconstruction provides new constraints on the low-energy theory and can rule out candidate EFTs that pass all previously known local lattice and anomaly consistency conditions. Separately, for theories admitting geometric tensor bases, we explain how the same reconstruction determines the complete Mori cone of the corresponding Kähler surface.

We compute the energy-energy correlator in a state created by a heavy canonical operator of scaling dimension $\Delta_H$ in $\mathcal{N}=4$ $SU(N)$ SYM, at fixed $N$ and arbitrary values of the large charge 't Hooft coupling $\lambda \sim \Delta_H g_{\rm YM}^2$. The state created by the canonical operator triggers spontaneous breaking of conformal symmetry and the Higgs mechanism, with squared W-boson masses proportional to $\lambda$. We start with the known finite-coupling result for the underlying four-point function of local operators, perform the detector and Fourier transforms and express the resulting energy-energy correlator as an infinite OPE sum in the source-detector channel, which we then analyze both numerically and analytically. We show that the finite-coupling energy-energy correlator exhibits a hierarchy of distinct physical regimes as a function of $z=(1-\cos\theta)/2$, where $\theta$ is the angle between the detectors. A small-angle vacuum-dominated behavior at $z\ll\lambda^{-1}$ is followed by a non-monotonic medium-induced transient behavior at $\lambda z \sim1$. A large charge jet regime follows, where the energy-energy correlator displays a power-law behavior $\sim1/(\lambda z^3)$ for $\lambda^{-1}\lesssim z \lesssim \lambda^{-1/3}$, before approaching an angle-independent plateau at larger angles.

We construct the entanglement entropy of a general scattering process between one particle species (denoted as $A$) and the rest of the final state. Assuming a pure initial momentum eigenstate, we show that the reduced density matrix in particle $A$'s Fock space is block-diagonal in zero-, one- and multi-particle states, and is diagonal in the momentum basis for the one-particle state. As a result, we could write down the Von Neumann entropy of particle $A$, $S_A$, in terms of scattering probabilities and differential cross sections, assuming no more than one particle $A$ is produced in the final state. $S_A$ contains the information of both the total scattering probabilities (or cross sections) and the differential distributions — the latter depends on a phase-space resolution factor as a result of the infinite-dimensional momentum Hilbert space. Our result is general and model-independent since we consider the full final state from time evolution ($S|i\rangle$) rather than a specific outcome, and is applicable as long as the probability for producing multiple particle $A$ is subleading. We also obtain the $n\geq2$ Tsallis and Rényi entropies in our framework and find out that, at the leading order, they are proportional to the total scattering probability and carry no differential information.

Koide and Alikhanov proposed intriguing empirical relations among charged-lepton masses and neutrino mass splittings, respectively. We present mass-matrix textures that realise these relations and can jointly account for the observed lepton mixing angles, while yielding predictive correlations among them and the neutrino CP phases.

We construct the general theory of a spin-1 field propagating on an inflationary background consistent with scale invariance, rotations, Bunch-Davies conditions and microcausality. Our Boostless Proca theory generalises the usual massive Proca theory to a Lagrangian with 5 free parameters: 4 corresponding to parity-even terms and a single parity-odd term. We impose three degrees of freedom from the outset and find that microcausality, the statement that field operators vanish outside the lightcone, requires the kinetic terms to be gauge invariant. We couple this spin-1 state to the inflaton and study the signatures it imprints on cosmological correlators. We find no new signals for the bispectrum meaning that the known signals are the most general thereby providing a very clean model-independent probe of new physics in this leading form of non-Gaussianity. For the trispectrum and higher-point functions, the boostless Proca theory produces new shapes with all 5 parameters in principle measurable.

We show how to construct perturbative effective field theories for strong phase transitions, where the standard tools of high-temperature dimensional reduction fail. By identifying the relevant power counting relations for the couplings, masses and background fields, we construct a controlled perturbative expansion adapted to this regime. We find that the order parameter field remains light at the transition, so that there is a controlled derivative expansion, even though large external fields need to be resummed. The resulting effective field theories for strong phase transitions live in three dimensions and have nonpolynomial field dependence. Applying our framework to a two-scalar model, we verify renormalisation scale cancellation through next-to-next-to-leading order and find decreasing corrections to the latent heat as the perturbative order is increased. Extending to include fermions and gauge fields, we identify a broad class of models in which strong-transition thermodynamics are systematically improvable.

We use the massive spinor-helicity formalism to describe a novel construction for massive spinors which allows one to connect the many choices of bases useful in the representation of amplitudes involving massive particles, and we use this to derive a new formulation for the general BCFW shift that is valid regardless whether or which of the particles involved are massive or massless. This formalism should help facilitate a more coherent implementation of on-shell recursion for computing amplitudes involving massive particles in four dimensions.

Hawking amplitudes provide a new way of determining the Hawking spectrum of black holes, using on-shell techniques borrowed from the literature on scattering amplitudes. In this paper, we investigate the interplay between the semi-classical and weak-field approximations previously used to compute Hawking amplitudes. We find that these limits do not necessarily commute, highlighting subtleties with the saddle point analyses governing the semi-classical limit. Resolving these issues allows us to compute semi-classical Hawking amplitudes in a range of black-hole backgrounds, including Tangherlini, Reissner-Nordström, and Hernquist metrics. Moreover, we describe the saddle-point contributions dominating Hawking amplitudes for different energies and propose a new method for determining the temperature of the resulting thermal spectrum based on Stokes lines of Hawking amplitudes.

We argue that the scattering amplitude of a single minus helicity gluon with arbitrarily many positive helicity gluons is topological. The amplitude is constant in chambers of kinematic space, its resonances are located at walls and its factorization is determined by wall-crossing. Yangian invariance dictates the amplitude to be determined by a 2d null Wilson loop that can be lifted into a positive and transverse 3d link. By reinterpreting wall-crossing and the Weinberg soft theorem as skein relations and Reidemeister moves of the subknots, we construct a state-counting description consisting of adding the `corners' of their HOMFLY-PT polynomials. Beyond the classical limit, we argue that this provides a conjectured but precise connection to topological field and string theory. The new formula is rigorously derived via a Lean-formalized dependency graph (DAG) as detailed in a companion paper, laying out the precise assumptions including Reidemeister III invariance. It is further tested exhaustively, including novel `star' kinematics where the amplitude and state count are shown to become Catalan numbers, in agreement with knot theory literature.