Papers

Giant graviton expansions express finite-rank corrections to supersymmetric indices in terms of indices for wrapped D3-branes. We give detailed algebraic proofs of two previously proposed relations for four-dimensional $\mathcal N=4$ $U(N)$ super-Yang–Mills theory. The first is the Gaiotto–Lee single-sum expansion of the full superconformal index, proved by Hall–Littlewood orthogonality and an elementary calculation of operator traces. The second is the symmetric double-sum expansion of the flavored Schur index, proved by factorizing its exact free-fermion mode product. We specify the analytic continuation of the brane indices and justify the sums coefficient by coefficient. The two proofs apply to different expansion prescriptions and do not establish the full three-species expansion of Imamura. We discuss the additional physical and mathematical questions raised by that expansion and by the modular properties of the Schur index.

We take a first step in identifying the superconformal quantum mechanics dual to supersymmetric AdS$_2\times$S$^2$ solutions. We focus on the Type IIB solutions of the form AdS$_2\times$S$^2\times$CY$_2\times\Sigma$ that preserve eight supercharges, with $\Sigma$ a two-dimensional space parametrised by $(x_1,x_2)$, and read off their brane content, a D1-D5-NS5 intersection with D3 and D7 flavour branes. We propose that their dual $\mathcal{N}=4$ quantum mechanics is organised over a two-dimensional lattice of cells in $\Sigma$. Namely, it consists of copies of the linear quiver along $x_1$ dual to the U(1)-invariant solutions of the class, one for each interval along $x_2$, with ranks given by the D1 and D5 charges of the corresponding cell. Its central charge agrees with the holographic one at leading order. We show that the family of SL$(2,\mathbb{R})$ non-Abelian T-duals of the AdS$_3\times$S$^2\times$CY$_2$ solutions of massive Type IIA supergravity, constructed in previous work, belongs to this class, as does the SL$(2,\mathbb{R})\times$SU$(2)$ non-Abelian T-dual of AdS$_3\times$S$^3\times$CY$_2$, and work both out in detail. For both we propose global completions that introduce additional D3 and D7 branes. Along $x_2$ we interpret the fundamental strings stretched between the colour branes and the additional D3 and D7 branes as baryon vertices. Finally, we extend this proposal from the non-Abelian T-duals to the solutions of the class whose defining functions factorise in $x_1$ and $x_2$, including those in which the AdS$_2$ and S$^2$ factors have the same warp factor.

The LZ collaboration has recently reported a single nuclear-recoil event at $E_R=248\pm23_\text{stat}\pm23_\text{sys}$ keV, observed in a 2.84 tonne-year exposure with a local significance of $3.4\sigma$, pointing towards an inelastic dark matter (DM) interpretation. We explain this event within a gauged $U(1)_X$ hidden-sector model, spontaneously broken by a singlet scalar whose vacuum expectation value (VEV) gives rise to: (i) gauge boson mass, (ii) a small Majorana mass for the vector-like singlet fermion, the DM candidate, charged under the new symmetry, which splits the fermion into two pseudo-Dirac states (mass splitting proportional to the scalar VEV) thus resulting in a purely off-diagonal vector current, (iii) the frequency and the amplitude of the GW signal arising from the hidden sector symmetry breaking via first-order phase transition (FOPT). The symmetry-breaking scale thus provides a multi-messenger probe connecting terrestrial direct-detection kinematics at the LZ and early-universe FOPT thermodynamics while obtaining thermal DM relic abundance. We delineate the viable parameter space compatible with the LZ event, correct relic density, and detectable GW signals in the low frequency regimes at future interferometers like $\mu {\rm ARES}$ and THEIA while satisfying existing cosmological, astrophysical, and terrestrial bounds.

We study the contributions of half-BPS surface defects to supersymmetric Casimir energy and the universal logarithmic term of supersymmetric Rényi entropy in four- and six-dimensional SCFTs. Using equivariant integration of defect anomaly polynomials and its extension to supersymmetric Rényi backgrounds, we obtain closed expressions for these observables in terms of defect 't Hooft anomalies. For Gukov–Witten defects preserving transverse rotations in four-dimensional $\mathcal{N} = 4$ super Yang–Mills theories, both observables depend on a single R-symmetry anomaly. For $\mathcal{N} = (0, 4)$ defects in six-dimensional $\mathcal{N} = (1, 0)$ theories, additional terms arise from the gravitational anomaly. We provide complementary checks using chiral algebras, five-dimensional localization, and holographic probe branes at large $N$, while localized chiral fermions reproduce the gravitational-anomaly contributions. The framework also recovers Wilson-surface results in six-dimensional $\mathcal{N} = (2, 0)$ theories.

We consider the matrix model of a seven-dimensional quantum space built from concentric fuzzy $CP^3$'s of increasing matrix size, and show that its continuum limit is the metric cone $C(CP^3)$ over $CP^3$, not flat $R^7$. Every ingredient is fixed before any comparison, so this geometry is a prediction rather than an input. The two geometries agree in the $s$ wave ($p=0$) but separate in the higher angular sectors (harmonics on $CP^3$ of degree $p\geq1$): in each sector tested, the spectrum of the free Laplacian converges at second order to that of the cone, and at 20480 layers the cone is matched to $1\times10^{-9}$ for $p\leq8$, whereas flat space misses by 8-18%. The free propagator converges to that of the cone at the same order, and heat diffusion reproduces the $r^6$ measure and the Bessel spectrum of the cone. The maps between neighbouring layers are obtained in closed form from the polar decomposition of the second-quantized Schwinger-boson lift, using a known operator identity, and coincide with the Kováčik-Tekel coefficient-copying prescription. For $CP^1$ the construction reduces, away from the outer boundary, to the Kováčik-Tekel fuzzy onion. Modes along the twistor fibre are exactly degenerate with the harmonics on $S^4$.

Replacing the circle by a manifold leads to current Lie algebras and their central and derivation extensions. We separate the coefficient algebra, harmonic analysis and geometric data. Differentials modulo exact forms describe central extensions; divergence-free vector fields give explicit cocycles, whose compatible derivations satisfy a stabilizer equation. Compact examples include the three-sphere and its current–Virasoro extension. We also explain the analytic qualifications for SL(2,R) and its symmetric space and the role of transported multiplication in soft geometries. The recent harmonic constructions of Campoamor-Stursberg, Marrani and Rausch de Traubenberg are compared with the cohomological work of Coquereaux, Frappat, Ragoucy and Sorba and Castellani's loop geometry and infinite-dimensional free differential algebras. A coefficient-algebra construction connects currents to higher brackets and clarifies the additional requirements of a dynamical theory. For Lie algebras of order F, central extensions obey coupled binary and symmetric F-ary conditions, with explicit examples and obstructions.

We study certain simple affine vertex algebras $L_{-1-h/6}(\mathfrak{g})$ from rank-one Argyres-Douglas theories, where $\mathfrak{g}$ is a non-simply-laced simple Lie algebra and $h$ is its Coxeter number. For $L_{-3}(F_4)$, we determine the maximal ideal of $V^{-3}(F_4)$, Zhu's algebra, and the associated variety. We also classify the irreducible highest-weight $L_{-3}(F_4)$-modules and determine the characters of its irreducible ordinary modules. The associated variety is $\overline{\mathbb{O}}_{\widetilde A_1}$, and the level $-3$ is totally collapsing for the orbit $\mathbb{O}_{\widetilde A_1}$. The Poisson coinvariants of the $C_2$-algebra of $L_{-3}(F_4)$ are isomorphic to $\mathbb{C}[\ell]/(\ell^5)$, where $\ell$ is induced by the conformal vector. Consequently, the characters of ordinary $L_{-3}(F_4)$-modules satisfy a fifth-order modular linear differential equation. We also give modular linear differential equations of orders five and eleven satisfied by the characters of ordinary modules for $L_{-2}(B_3)$ and $L_{-2}(G_2)$ respectively.

We study the sharp constant in the differential inequality \[ I(t)I''(t)\geq c\,[I'(t)]^2 \] for Fisher information along the probability-normalized heat flow on $\mathbb R^2$. The unrestricted log-convexity value $c=1$ is false in two dimensions, whereas the known square-root convexity theorem gives the universal value $c=1/2$. We construct an exact, machine-verifiable sum-of-squares certificate proving the stronger universal bound \[ c\geq \frac{231691}{250000}=0.926764. \] Together with an independent exact Fourier/Gaussian-envelope construction, this gives \[ 0.926764\leq c_*<0.94176665012062, \] where $c_*$ is the sharp constant for positive-time Gaussian convolutions of arbitrary probability measures on $\mathbb R^2$. We formulate the proof in explicit two-dimensional index notation. The lower bound follows from an exact rational polynomial identity involving a strictly positive denominator, a weighted total derivative, and eleven positive rational Gram matrices. All $491$ recorded leading principal minors are strictly positive and the complete polynomial identity has zero residual. No symmetry, log-concavity, finite-variance, or finite-entropy assumption is imposed on the initial measure. The sharp value remains open.

In this work we construct three-dimensional Chern–Simons gravity theories for the six resonant $JPZ$ algebras generated by the Lorentz generators $J_a$, translations $P_a$, and an additional Lorentz-like generator $Z_a$. The resonance condition together with the Jacobi identities leaves precisely six configurations arising from the semigroup expansions. Our main result is that three of them, $B_4$, $\widetilde C_4$, and $C_4$, are isomorphic to $iso(2,1)\oplus so(2,1)$, although they yield different gravitational realizations when we keep the original $JPZ$ field identification fixed. For each case $JPZ$, we determine the invariant tensors, gauge curvatures, Chern–Simons action, field equations, and the corresponding maximal-rank coupling sectors. The field equations can be written in the compact form $\Omega_\sigma\mathbf F=0$, which makes explicit how the additional field $h^a$ contributes to the curvature, torsion, and the remaining gauge-curvature components. We use the direct-sum isomorphisms to classify the local metric sectors and to relate them to known global and asymptotic solutions, while keeping the gravitational interpretation tied to the original $(\omega,e,h)$ fields.

We investigate the early-universe cosmological implications of Unimodular Gravity coupled to Power-Law Nonlinear Electrodynamics in the presence of quantum-corrected horizon thermodynamics derived from the principle of thermodynamic duality. By incorporating both logarithmic and inverse-area corrections to the Bekenstein-Hawking entropy, we derive modified Friedmann equations exhibiting novel $H^4$ and $H^6$ terms that represent genuine quantum gravity effects. We demonstrate that these higher-order corrections become dynamically significant in the high-energy regime of cosmic inflation, naturally modifying the slow-roll dynamics without requiring a fundamental inflaton potential. A comprehensive phase-space analysis reveals that the quantum corrections drive early-time de Sitter-like attractors, providing a robust mechanism for sustained inflationary expansion. Confronting the model with the Swampland program, we show that the correction factor $\mathcal{F}(H)$ modifies the effective slow-roll parameters, enabling the model to satisfy the Swampland de Sitter and Distance conjectures during the inflationary epoch. We calculate the inflationary observables, including the spectral index $n_s$ and the tensor-to-scalar ratio $r$, and demonstrate that the model's predictions are in excellent agreement with the Planck 2018 observational constraints. Our results suggest that thermodynamic duality-induced horizon corrections offer a viable and testable pathway for realizing successful inflation within a well-motivated quantum-gravitational framework.

We show that adding a dimension-six self-interaction to the Abelian-Higgs or Ginzburg Landau model results in a remarkable and rich structure of multi-vortex solutions. Besides the standard type I (attractive) and type II (repulsive) regimes, separated by the Bogomol'nyi-Prasad-Sommerfeld limit (BPS), we identify two new possibilities: type I-II vortices, which attract at short distances and repel at long distances; and type II-I vortices, with the opposite behaviour. Specifically, within the type II-I regime, multi-vortex solutions form chunks of the Abrikosov lattice or clusters. Conversely, in the I-II regime, axially symmetric multi-vortices are stable; nevertheless, depending on the model parameters and topological charge (winding number), they can be either the ground state or not.

The question of the link between the nucleon properties and the equation of state of ultra-dense matter, both being composed of quarks and gluons, is investigated by adopting a soliton model to describe internal nucleon properties and a direct mapping between nucleon and quark matter to obtain the equation of state of ultra-dense matter. We compare $\pi+\omega$ and $\pi+\omega+\rho$ soliton models and analyze the presence of a pressure singularity at the nucleon center due to the $\rho$ field. This singularity impacts the equation of state in ultra-dense matter. Only the pressure derived from the canonical energy-momentum tensor has a singularity, while the Belinfante pseudo-gauge transformation of the energy-momentum tensor generates an internal pressure without a singularity. We then investigate predictions for the equation of state of ultra-dense matter based on different prescriptions for the nucleon pressure. It is shown that none of the prescriptions agree with the thermodynamical pressure defined in uniform matter. The mismatch between any equation of state and the thermodynamical one questions the simplicity of the direct mapping between finite-size nucleon properties and uniform matter as well as the role of the nucleon surface in the internal energy density and the pressure.

We study Yang–Baxter deformations of two-dimensional sigma models on compact symmetric spaces $\mathrm{SU}(N)/\mathrm{SO}(N)$, with particular emphasis on their ultraviolet behavior. We claim that the ultraviolet fixed point is described by the $\mathrm{SO}(N,\mathbb C)/\mathrm{SO}(N,\mathbb R)$ non-compact WZW model together with $N-1$ compact free bosons. We determine the leading correction to this fixed point and identify it with the perturbation generated by the corresponding screening currents. We also extend our construction to the broader class of symmetric spaces of maximal rank.

The Brout–Englert–Higgs (BEH) mechanism can be formulated in gauge-invariant relational terms without assigning physical spontaneous breaking to a local gauge redundancy. We treat the gauge orientation of the Higgs field as dynamical internal reference data and describe the gauge connection relative to this Higgs frame. On a regular patch where the frame exists, the Higgs kinetic term induces a positive-semidefinite mass-squared quadratic form on the gauge-orbit directions and reproduces the standard tree-level vector masses. A complete Higgs frame yields a gauge-invariant relational connection, whereas a partial frame is defined only up to a stabilizer group $H$ and produces Higgs stiffness only along the coset directions $G/H$. In quantum field theory the normalized frame and relational connection are nonpolynomial composite variables; physical masses are therefore characterized through suitably renormalized gauge-invariant composite correlators, or through fully dressed operators in residual-charged sectors. Applying this construction to the electroweak theory, we show that the Higgs frame relationalizes the $SU(2)_L$ redundancy while leaving a residual electromagnetic $U(1)_{\rm em}$ Gauss law: $W^\pm$ and charged fermionic modes require electromagnetic dressing, whereas neutral channels admit local gauge-invariant interpolators. This formulation connects Higgs dressings, FMS composites, and internal quantum-reference-frame language while keeping local mass generation distinct from global symmetry realization and topological obstructions.

The static Love numbers of black holes vanish in classical, four-dimensional, asymptotically flat General Relativity. We study how this changes for the response of near-extremal Reissner–Nordström black holes to a minimally coupled massless scalar, at energies where the Schwarzian mode of the near-horizon throat fluctuates strongly. The black hole then responds as a quantum system with a spectrum of states. Its static response is a polarizability, given by virtual transitions between them. For $\ell=0$ the static Love number vanishes, by the shift symmetry of the scalar, but for multipoles $\ell\geq1$ the static Love numbers are nonzero: the finite rotational energy of the spin-$\ell$ intermediate states spoils the cancellation responsible for the classical result. Since the throat no longer has a classical geometry from which to read off a tidal response, we define it through the retarded Green's function, and compute its full frequency dependence at leading order in $r_+\omega$. Its conservative part requires renormalization: the near-horizon theory fixes the coefficient of its logarithm, and with it a dependence on the energy that no local term can remove, while its finite local terms are matching data of the four-dimensional theory. The dissipative part is finite and scheme independent. For $\ell\geq1$, it vanishes at low frequencies when the energy is below the rotational gap, while at the gap threshold it becomes non-analytic in frequency and produces a late-time $t^{-3/2}$ tail.

Via the Rindler method, we study holographic timelike entanglement entropy (TEE) for a general timelike interval in AdS$_3$/CFT$_2$ and flat$_3$/CCFT$_2$. The TEE is the pseudo entropy of a timelike interval. In the bulk, the imaginary part of the TEE comes from a timelike geodesic, but in the Rindler picture this geodesic has not been identified. After a Rindler transformation to a rotating BTZ black hole, the two spacelike extremal curves lie on the inner and outer horizons, and exchanging $l_u\leftrightarrow \ell l_\phi$ takes one to the other. We find the geometric meaning of the timelike extremal curve: a geodesic stretched between the two horizons. Its length, $i\pi\ell$, is independent of the interval, and it alone produces the imaginary part $i\pi c/6$. We follow the same procedure in flat space holography, where the spacelike curve sits on the cosmological horizon and the timelike curve lies between the cosmological horizon and timelike infinity. Evaluating the holographic TEE for a timelike interval in CCFT$_2$ on the plane, we find that, in contrast with the cylinder, the real and imaginary parts are equal.

We construct a three-parameter family of regular analytic supergravity solutions which are dual to (a) the $\mathcal{N}=2^*$ gauge theory on the four-sphere, and (b) $\mathrm{U}(1)^2$-invariant Janus interfaces in $\mathcal{N}=4$ SYM with or without the $\mathcal{N}=2^*$ mass turned on. To this end we employ a five-dimensional supergravity model coupled to six scalars which arises as a certain consistent truncation of type IIB supergravity on $S^5$. The curved domain wall solutions feature a hidden integral of motion which allows for their analytic treatment. We relate the three parameters of the solution to field theory sources and vevs and show how regularity of the solutions restricts their range. We briefly discuss the holographic evaluation of the one-point function of the field theory Lagrangian for our family of Janus solutions.

For the two-point function of the massless, minimally-coupled, real scalar field in Euclidean de Sitter space with $\lambda\phi^4$-interaction, we compute the leading-logarithmic terms in the invariant distance of the two-point function to $O(\lambda^2)$, which counts as the fifth subleading order (N$^5$LO) in the $\sqrt{\lambda}$-expansion. We show that the analytic continuation to Lorentzian signature coincides with the expansion of the analogous quantity computed in the stochastic formalism. We determine the large-order behaviour of the stochastic series expansion and prove its Borel summability, which suggests that the Euclidean theory can be used to extract the late-time behaviour of massless correlation functions in Lorentzian de Sitter space.

Every physical prediction of an event generator is a statement about the hadronic fluxes that can be recorded by particle detectors. By contrast, the formal backbone of modern event-generator precision is provided by the unobservable partonic final states of the parton shower, with hadronisation included as a model. We construct the probability distribution of the hadronic fluxes non-perturbatively, directly from detector operators acting on asymptotic hadronic states, and encode it in an event generator source functional. This distribution contains every measurement a detector can make, and is therefore what a generator must compute with precision, including the effects of hadronisation. Restricting the functional to the energy flow yields the parton shower source functional, which is infrared and collinear safe and contains every calorimetric observable, making it a natural object against which to assess parton-shower accuracy. We compute its logarithmic structure at one loop in $e^+e^-$ annihilation, finding it directly sensitive to kinematic recoil and hence to the recoil scheme of a parton shower. The parton shower functional depends on a continuum of low scales, one for each resolved direction, and in a toy model its logarithms cannot be entirely resummed within a factorisation whose evolution derives only from the high-scale physics. Our operator-based formulation opens the door to the study of event-generator-like systems in theories beyond QCD, including conformal theories such as $N=4$ super-Yang-Mills theory, and thereby offers a new route to non-perturbative insight into event generation.

We revisit the scenario of critical Higgs inflation, in which inflation is driven by the Standard Model Higgs boson with parameters chosen close to a critical point, giving rise to an inflection point in its potential. After reviewing this model, we perform a systematic study of its viability centered around three criteria: (1) consistency with electroweak-scale measurements, (2) ability to reproduce the cosmic microwave background (CMB) observables, and (3) sensitivity of the model predictions to unknown UV physics, based on a breakdown of perturbative unitarity. We first show that compliance with electroweak-scale measurements is controlled by the parameters in the Higgs potential at inflationary scales, also updating the literature values. We then demonstrate how for any choice of potential parameters, agreement with the CMB observables can be achieved through the choice of the nonminimal coupling, in both metric and Palatini formulations of gravity. However, we also find that there exist no regions of parameter space, in either the metric or Palatini formulations, in which compliance with all three physical criteria is possible. While this does not exclude the possibility of the Higgs field driving inflation, it means that predictions for any observable are in principle sensitive to the details of the model's UV completion.

Tidal Love numbers characterize the conservative response of compact objects to external perturbations and provide a powerful probe of their nature. While the static Love numbers of Schwarzschild, Kerr, and Reissner–Nordström black holes remarkably vanish, the tidal response of a generic Kerr–Newman black hole has remained unexplored due to the intrinsic coupling between gravitational and electromagnetic perturbations. Exploiting a recent breakthrough in the separability of these perturbations, we analytically determine the static tidal response of the most general stationary black hole in four-dimensional Einstein–Maxwell theory. For arbitrary multipole order, charge, and spin, we show that the entire matrix of conservative Love numbers vanishes, including the mixed gravito-electromagnetic couplings. We also compute the nonvanishing static dissipative response induced by frame dragging.

Timelike entanglement entropy provides a useful probe of holographic theoris, yet an explicit bulk realization of the modular flow underlying its timelike extremal curve construction has so far been lacking. We construct modular flows associated with spacelike and timelike intervals in AdS$_{3}$/CFT$_{2}$ and extend this framework to flat$_{3}$/CCFT$_{2}$. Beginning with the boundary symmetry generators, we explicitly derive the boundary modular flows and extend them into the bulk, providing a systematic procedure that relates bulk modular flows to the extremal curves and holographic (timelike) entanglement entropy. For spacelike intervals, the resulting bulk modular flows determine the extremal curves, whose integrated line elements reproduce the standard holographic entanglement entropy. We then generalize this approach to timelike intervals, explicitly constructing the modular flows whose fixed points reproduce the extremal spacelike and timelike curves which gives the holographic timelike entanglement entropy. To the best of our knowledge, this is the first explicit construction of the modular flow associated with a timelike extremal curve for a timelike interval. The same procedure is then carried over to flat$_{3}$/CCFT$_{2}$, which give rise to the holographic (timelike) entanglement entropy. Finally, we show that the flat space results obtained in this work can be recovered from their AdS$_3$ counterparts in the flat space limit.

While terrestrial colliders and fixed-target cosmic-ray interactions are bounded at center-of-mass (CM) energies $\sqrt{s} \lesssim \mathcal{O}(10^5)\,\text{GeV}$, we demonstrate that bound sub-parsec binary blazars form broad-band, beam-beam hadronic “Cosmic Colliders”, overcoming such limitation. Driven by modest jet misalignments ($\theta_{\rm mis} \sim 1^\circ - 6^\circ$), co-streaming proton beams collide at CM energies reaching $\sqrt{s} \sim 10^{10}\,\text{GeV}$ - six orders of magnitude above the Large Hadron Collider. Operating in a strictly optically thin regime ($\tau_{pp} \ll 1$), the system performs a continuous CM energy scan, probing asymptotic QCD scaling, gluon saturation, and Froissart unitarity, while opening a possible high-sensitivity window into physics beyond the Standard Model. Secondary PeV-EeV neutrinos and sub-TeV $\gamma$-rays fall directly within reach of current and planned observatories such as LHAASO, CTAO, IceCube, and GRAND, establishing binary blazars as laboratories for physics at the ultimate energy limit.

Black-hole interiors are hidden from exterior observers, yet their geometry can enter the high-overtone spectrum of linear perturbations. We study how this spectrum encodes metric and supporting-matter information in analytic Einstein–Maxwell–dilaton black holes. Coupling a neutral spectator to the dilaton at fixed UV dimension provides a matter-sensitive channel alongside the momentum response. For real-endpoint spacelike connections, the momentum response and mass-label dependence separate the metric exponents from the signed dilaton slope. Near the causal threshold, a complex endpoint controls the spectral family: the mass profiles approach a common value, producing a shared fractional correction, while regular propagation retains label dependence. This mechanism is present at criticality without an inner horizon and continues locally into timelike interiors. Exterior numerical spectra support the reconstruction and the leading complex-endpoint responses. Local scaling and probe coupling set the candidate responses, while wave connection determines their imprint on the exterior spectrum.

We present a unified theory-to-simulation framework for self-interacting dark matter (SIDM), combining a self-contained introduction to its particle-physics foundations and representative benchmark models with an explicit, systematic mapping to simulation inputs and validated numerical implementations in the moving-mesh code AREPO-2. We characterize representative elementary and composite dark-sector models through their particle content, symmetries, interactions, production mechanisms, and constraints. We then establish an explicit mapping from their microscopic properties to the inputs required for structure-formation simulations, including modifications to cosmological initial conditions, internal-state mass splittings and populations, reaction networks, velocity- and angle-dependent cross sections, dissipative energy loss, and decay rates and recoil kinematics. Building on the efficient, scalable SIDM infrastructure introduced in our companion work, we implement isotropic and anisotropic self-scattering with constant or velocity-dependent cross sections, multi-state and inelastic reactions, and dissipative scattering, as well as a dedicated DM decay module. We validate the implementations through beam-lattice deflection experiments, thermalization and uniform-box decay tests, isolated-halo gravothermal core-collapse simulations, and cosmological box and zoom-in simulations. The tests reproduce analytical predictions and published inelastic and dissipative benchmarks, with agreement across numerical schemes. The resulting framework provides a common reference for researchers across disciplines and a practical route from microscopic dark-sector theories to nonlinear astrophysical predictions beyond standard isotropic, elastic SIDM.

We study the conformal coupling in the torsion-free Palatini formulation with an ordinary scalar kinetic term. Tuning the curvature coupling cannot restore Weyl invariance in a Palatini theory with an ordinary scalar kinetic term because, for an independent and inert connection, the scalar-curvature term is separately Weyl-invariant, and no finite curvature coupling cancels the Weyl variation of the kinetic term. This can be demonstrated by evaluating the energy-momentum trace on the scalar equation of motion and noting that it is explicitly independent of the Palatini coupling. Eliminating the connection, we construct a map between the curvature coupling and the effective coupling for the equivalent metric theory, and demonstrate that the scalar continues to propagate even if the reduced kinetic coefficient vanishes. We also show that it becomes a Weyl compensator with a scale-invariant potential only in the rescaled infinite-coupling limit, which in four dimensions is directly related to Palatini ${\cal R}^2$ gravity. We calculate the running of the couplings at one loop, and we find that the conformal shift in the metric-curvature coupling's beta function generates a metric-curvature coupling on a fixed metric-affine background, whereas the independent-curvature coupling runs homogeneously. Furthermore, we follow an alternate prescription in which the connection is allowed to respond to the scalar fluctuations, which results in a different scalar Hessian and therefore different beta functions. Nonetheless, we find that both prescriptions admit the formal infrared limit $(\xi_{eff},\lambda_{eff})\to(1/6,0)$ through different limits of the original couplings in the case of positive perturbative quartics. Finally, we note that trajectories starting on the positive gravitational branch encounter a vanishing gravitational coefficient at a finite scale before this endpoint.

Hydrodynamics as an effective field theory (EFT) has been immensely successful for predicting the behaviour of time-ordered correlation functions in the long-time, large-distance regime. In this paper, we analyse the predictions of hydrodynamics for scrambling as probed by out-of-time order correlators (OTOCs). To do so, we consider an all-derivative order generalisation of the Schwinger-Keldysh EFT of hydrodynamics extended to a four-fold time contour required to capture OTOCs. A crucial ingredient of the construction is a local SL(2,R) symmetry, which has previously been suggested as a mechanism for scrambling. We also derive this exact EFT from the microscopic formulation of the maximally chaotic low-temperature limit of the SYK lattice, thereby determining all transport coefficients for this model. As a novel application, we compute the OTOC of energy currents, find that its exponential growth saturates the chaos bound, and match it to expectations based on a shockwave (or scramblon) effective description. Our work shows that the universality of hydrodynamics degrees of freedom extends beyond traditional time-ordered correlators to more complex observables such as OTOCs.

We study the coupled diffusion of baryon number, electric charge, and strangeness in hot and dense quark matter using a three-flavor Nambu-Jona-Lasinio model with self-consistently generated constituent quark masses. The complete diffusion matrix is evaluated within a relaxation-time kinetic approach, including its diagonal and off-diagonal components. We find that the off-diagonal transport coefficients exhibit distinct temperature and baryon-chemical-potential dependence associated with the flavor-dependent composition of the charge carriers. We further investigate generalized charge diffusivities and mobilities obtained from the corresponding susceptibilities. At finite baryon chemical potential, the baryon and strangeness mobility scales cross, reflecting the different density dependence of their transport coefficients and susceptibilities. The results provide model benchmarks for coupled conserved-charge transport in baryon-rich QCD matter.

General Parallel Relativity is a dynamically equivalent formulation of Einstein gravity in which the parallel frame supplies explicit boundary reference data. In this formulation, finite-region energy-momentum and horizon entropy arise as distinct Hamiltonian surface charges. Diffeomorphisms along canonical frame directions define a quasi-local energy-momentum including a matter surface term, while normal-plane boosts at a smooth horizon give entropy. These covariant formulas are applied to the Reissner-Nordström black hole and to a dilatonic charged black hole. In both examples, the matter contribution and its Legendre transform complete the Misner-Sharp mass into the Hamiltonian energy appropriate to the chosen electromagnetic boundary datum. The resulting horizon charges satisfy the thermodynamic relation obtained independently from the Euclidean boundary action.

We recall a 1987 paper written by Volovich and our subsequent work with Okada which established the Feyman rules for the p-adic string and the related non-local field theory which found diverse physical applications. We add some memories of visits to Moscow during 1989-91.