Papers

We study phase diagrams of charge-conserving `class A' non-interacting fermions, focusing on the trivial phase in various dimensions. Such phases are usually termed `featureless' to distinguish them from those others with either symmetry-broken or topological order. We show that the presence of non-trivial topological families of states, including charge pumps and their generalizations, results in phase diagrams being endowed with non-trivial topological textures that can be visualized through Berry phases and their higher-dimensional generalizations. We show that for non-interacting fermion systems with translation invariance, these `higher' Berry phases can be computed using integrals of non-abelian Chern-Simons forms of the Berry-Bloch connection over momentum and parameter spaces. Singularities in these textures correspond to gap-closing loci of `diabolical points', which represent the obstruction to contracting topologically non-trivial families of states, and bulk-boundary correspondence results in a locus of robust boundary modes that terminate at the bulk diabolical points. In the presence of finite chemical potential, we argue that the edge modes are generically robust without any need for fine-tuning for two and higher dimensions, whereas in one dimension they are `estranged' in the phase diagram, i.e. appearing at different parameter values for different edges. We demonstrate our results by constructing several microscopic models of non-interacting fermions. We argue stability to interactions and explore proximate phase diagrams by mapping to continuum field theories.

We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions decay at each singularity, leading to a rich structure of boundary value problems. We derive the weakest quantization conditions compatible with decaying behavior at both singularities, and formulate these conditions in terms of the associated monodromy data. In doing so, we prove the quantization conditions predicted by the topological string/spectral theory duality for a family of deformed Schrödinger equations. More generally, our results point to a hierarchy of spectral problems interpolating between the minimal conditions studied here and the maximally decaying boundary conditions of the $N$-particle quantum Toda chain.

We study a local patch of an axion-like dark sector in Minkowski spacetime, containing an initially homogeneous and isotropic non-Abelian $SU(2)$ condensate, and a real pseudoscalar field $\chi$, coupled to an Abelian $U(1)$ gauge field which could be that of usual electromagnetism. The pseudoscalar couples directly to both gauge sectors through Chern-Simons interactions, while the $U(1)$ field couples to the $SU(2)$ condensate only indirectly, through the pseudoscalar. We show analytically that a homogeneous oscillating $SU(2)$ background $Q(t)$ acts as a periodic source for $\chi$, generating a homogeneous oscillatory condensate $\dot{\chi}$ that in turn modulates the frequency of the $U(1)$ helicity modes. In the linear regime this produces a Hill equation, and when the first harmonic dominates it reduces to a Mathieu equation. We derive the approximate resonance conditions, the leading Floquet exponent, and the conditions for a two-stage enhancement $Q \to \chi \to U(1)$. We also highlight an important point: in the exactly periodic, zero-bias limit, the indirect resonance is not intrinsically chiral, because the two Abelian helicities are related by a half-period time shift.

We return to and refine Zwiebach's formulation of closed string field theory (CSFT) built around non-critical backgrounds [1,2], restricting our attention to genus zero. The structure involves a special string state $F$ that encodes the failure of worldsheet BRST invariance, and a metric-dependent descent operator $\mathcal{B}$ adapted to the Weyl frame. We construct the mixed moduli spaces needed for the classical BV action, prove their existence, and extend the Sen-Zwiebach background independence argument to first order off of the conformal locus. We apply the formalism to the mildest deviation away from criticality - worldsheet CFTs with nonzero central charge: we consider both D=26-$\epsilon$ dimensional flat space and linear dilaton profiles in bosonic string theory, focusing for simplicity on building solutions that depend on only one of the D dimensions.

Inspired by the poles-zeros duality of Green's functions that appears in transitions into Mott-insulating phases in strongly correlated condensed matter systems, we propose a semi-holographic approach to Mott insulators. In this model, a fundamental fermion is coupled to a large-$N$, strongly interacting sector that generates a self-energy for the fundamental fermion's Green's function. This coupling amounts to a hybridization of the fundamental fermion with a strongly correlated fermionic composite. Within the holographic framework, at large $N$, the Green's function of the composite fermion naturally exhibits a poles-zeros duality. Zeros of the Green's function are caused by the poles of the self-energy that correspond to collective many-body excitations of the holographic strongly interacting sector. We calculate the spectral function of the fundamental fermion, from which we characterize the semi-holographic metallic and the Mott-insulating phases. In addition to the new physical interpretation of the zeros, our analysis yields a well-defined picture of the poles-zeros duality in terms of the freedom to choose between standard and alternative quantization in the strongly coupled sector.

We prove a version of the completeness hypothesis that follows from the coexistence of symmetry and gravity: tree-level gravitational scattering mandates single-particle states in all possible irreducible representations of the symmetry group constructible from a single seed charge. Our main assumption is that the leading high-energy behavior of scattering is universal irrespective of charge, thus satisfying the equivalence principle. Curiously, we discover that these newly-deduced states contribute democratically - that is, with equal interaction strengths - to scattering.

The “holography of information” (HoI) principle argues that gravity can encode information redundantly in asymptotic observables. Although HoI is ultimately a nonperturbative claim, its standard motivation uses semiclassical gravitational constraints, the boundary nature of the Hamiltonian, and vacuum-sector cyclicity. We ask what happens when the same semiclassical path-integral reasoning allows topology sums that generate baby-universe or $\alpha$-sector data. Our analysis is conditional: such sectors need not survive in every unitary completion, and the Baby Universe Hypothesis of McNamara and Vafa instead suggests $\dim\mathcal H_{\rm BU}=1$ in consistent $d>3$ quantum gravity. If $\mathcal H_{\rm BU}$ is nontrivial, as in the Marolf–Maxfield formulation and in ensemble-like examples such as JT gravity, then HoI is naturally refined to an $\alpha$-sectorwise statement, $\overline{\mathcal A_\infty^{(\alpha)}|0_\alpha\rangle}=\mathcal H_\alpha$, rather than completeness on the full topology-summed Hilbert space. In a fixed $\alpha$-sector, HoI may obstruct AMPS factorization and allow a smooth horizon; in an unconditioned topology-summed state, the sector-independent obstruction is not automatic. A Bell-pair diagnostic shows that a sector-independent smooth interior requires aligned interior reconstructions, or access to the sector label. Thus the HoI-based absence of firewalls becomes conditional on global sector data, in tension with the generally covariant expectation emphasized by Bousso that horizon normalcy should be determined by local semiclassical geometry. If the exact theory collapses $\mathcal H_{\rm BU}$ to one dimension, the obstruction discussed here is absent.

In the standard thermal relic scenario, dark matter remains in chemical equilibrium with the Standard Model radiation bath until freeze-out occurs at $T \sim m_X/20$, where $m_X$ is the dark matter mass. In this familiar class of models, the observed relic density is obtained for annihilation cross sections of order $\sigma v \sim 10^{-26}$ cm$^3$/s. We show that comparable cross sections can naturally be realized in hidden-sector models in which the dark matter and Standard Model sectors decouple at a very high temperature, $T \gg m_X$, and subsequently evolve with separate thermal histories. Despite this decoupling, the two sectors have similar temperatures during freeze-out, leading to the usual thermal relic abundance. As a consequence, the coupling between the Standard Model and hidden sectors can be extremely small, potentially placing direct detection and collider signals far below foreseeable sensitivities.

We investigate a non-relativistic realization of the boostless cosmological collider in a scenario where inflationary interactions are mediated by a massive tilted-ghost spectator field. Unlike standard boostless collider constructions, in which the characteristic non-Gaussian signatures are mainly generated by boost-breaking interaction vertices, the dominant effect in the present framework arises directly from the propagation of the spectator modes. Non-relativistic corrections deform the bulk mode functions, inducing a tilt that modifies the in-in correlators and generates a distinctive collider signal. The resulting squeezed-limit non-Gaussianity reproduces the qualitative structure of boostless cosmological-collider signals while originating from a fundamentally different dynamical mechanism. A central feature of the construction is the emergence of an effective chemical-potential-like parameter that controls the relative weight of the two late-time oscillatory branches. However, the tilted-ghost mode exhibits distinctive dynamical features and does not correspond to a conventional chemical-potential deformation. Depending on the sign of the tilt, the corresponding non-Gaussian signal can be either enhanced or suppressed. We show that the tilted-ghost scenario provides a simple effective framework in which boostless-collider phenomenology and chemical-potential-like branch asymmetries arise naturally from non-relativistic propagation effects.

Most of the laws of Nature involve derivatives up to the second order. Ostrogradski was the first to seek a formulation of the equations of higher-order derivatives. He extended Hamilton's equations by considering Lagrangians that depend on higher-order derivatives of generalized coordinates. The Hamilton-Ostrogradski formulation served as the basis for later studies with higher-order derivatives. However, the Hamilton-Ostrogradski formalism is rarely discussed in textbooks or the pedagogical literature. This motivated us to show how the Hamilton-Ostrogradski formalism can be applied it to the Pais-Uhlenbeck oscillator. We hope that the approach presented in this work can serve as a basis for discussion in advanced classical mechanics courses.

In this paper we propose a novel unified cosmological model that connects a pre-inflationary epoch, starting at the Planckian time, with the onset of inflation within a single scalar-field framework. The pre-inflationary phase is characterized by a decelerated expansion with an increasing comoving Hubble horizon, followed by a gradually transition to an accelerated inflationary regime. This early dynamics leads to a modified causal structure that naturally accounts for the suppression of large-angle $(\theta \gtrsim 60^\circ)$ correlations in the cosmic microwave background (CMB) reported by the satellite PLANCK. We study the quantum fluctuations of the scalar field using the Mukhanov-Sasaki formalism and a canonical quantization procedure based on energy minimization. We find that the vacuum state is well-defined only for sub-horizon modes at the onset of inflation, which induces a natural cutoff in the primordial power spectrum. The resulting spectrum exhibits a suppression at large scales while remaining nearly scale-invariant at small scales. In the appropriate limit, the model recovers the standard de Sitter result, in agreement with current observational constraints. These results highlight the relevance of pre-inflationary dynamics for addressing large-scale anomalies within a consistent inflationary framework.

Many approaches to quantum gravity require replacing the traditional black hole geometry with an Exotic Compact Object (ECO), which has a large but not infinite redshift at its surface. We argue that near the ECO surface, the vacuum Einstein equations imply a metric that is chaotic, with increasingly large oscillations as we approach the surface. This behavior is analogous to the `cosmic billiards' found in the BKL analysis of cosmology near the big bang. For the ECO, some of the potential walls of this billiards change sign to become `cliffs', resulting in a runaway behavior where some compact directions squeeze to zero size. In string theory such squeezing yields a natural continuation to the interior geometry of fuzzballs, where compact directions collapse to create monopoles.

We numerically approximate the Tomita-Takesaki modular operator for local subalgebras of the 1+1-dimensional massive Majorana field. Our method works at the one-particle level with a discretisation of time-0 data in position space. The local subspaces we consider are associated with one double cone and with the disjoint union of two double cones. In order to avoid boundary effects, we primarily choose the overall spacetime to be a cylinder; different choices of boundary conditions (antiperiodic and periodic) are considered. We compare our numerical results to known analytic expressions in the massless case. It turns out that the modular operator has a non-trivial dependence on the mass. In the case of two double cones, the modular generator does not only have ”local” contributions (supported on the diagonal in configuration space) but also ”bilocal” terms (connecting the two double cone regions); we find the latter to be less prominent at higher masses, in line with expectations.

TeV string-mass-scale strings have been excluded experimentally at colliders, as their effects have not been observed at the Large Hadron Collider (CERN). On the other hand, higher-scale string theory, with mass scales typically close to the Planck scale, is often regarded as experimentally inaccessible due to the enormous energies required for direct tests, and far beyond the reach of present or foreseeable particle accelerators. Nevertheless, the early Universe may provide an indirect observational window for high-string scale through imprints left on the Cosmic Microwave Background (CMB). In this work, building on previous studies, we reexamine temperature and polarization angular correlations as probes of the geometry and topology of the pre-inflationary Universe. We focus in particular on two-point correlation functions at large angular scales, where signatures of nontrivial spatial topology may survive as relics of primordial physics. We investigate the observational consequences of toroidal compactification and analyze their impact on the primordial power spectrum of the CMB provided by the Planck satellite. Within the current experimental and theoretical uncertainties, we identify a possible indication closely related to spatial-parity breaking, consistent with the presence of six spatial extra dimensions in the early Universe, compactified at the GUT epoch before the start of inflation. Finally, we extend our framework to B-mode polarization, highlighting its potential as a sensitive probe in forthcoming ground-based and space-borne experiments with unprecedented precision.

Using a recursive solution of the Einstein equations, we consider the perturbative expansion of the metric corresponding to a Kerr black hole. Because the metric is a function of two parameters, Newton's constant G and the Kerr spin parameter a, the perturbation theory naturally becomes a double expansion. In harmonic gauge the recursion relations can be solved to arbitrarily high orders in these two expansion parameters but to re-sum the series into the closed-form harmonic gauge metric requires the introduction of terms that are redundant and correspond to the addition of harmonic functions to the coordinates. Issues related to dimensional regularization of Fourier transforms are explained in detail.

We propose the rare SM Higgs decay $H\to b\bar b b\bar b$ as a probe of the structure of Higgs interactions with bottom quarks and gauge bosons, and as a baseline for searches for new physics producing four-bottom final states in Higgs decays. We compute the leading contributions to this decay, including the dominant $H\to b\bar b g\to b\bar b b\bar b$ topology, the sizeable $H\to ZZ^\ast\to b\bar b b\bar b$ channel, and the loop-induced $H\to gg\to b\bar b b\bar b$ contribution. We find a branching ratio of order $1.6\times10^{-3}$ and show that destructive interference among the leading amplitudes is phenomenologically relevant. We demonstrate that this decay can be probed in associated Higgs production at both the HL-LHC and the ILC. For $pp\to WH\to Wb\bar b b\bar b$ at $\sqrt{s}=14$ TeV, we use a multivariate analysis based on boosted decision trees to exploit correlations among the four-$b$ kinematic observables. At $3000~{\rm fb}^{-1}$, the statistical significance reaches about $3.5$, while a tighter high-purity working point gives $S/B\simeq5\%$ with significance close to $3\sigma$. A combined high-luminosity LHC dataset could therefore make this rare decay observable. For $e^+e^-\to ZH\to Zb\bar b b\bar b$ at the ILC with $\sqrt{s}=250$ GeV, we demonstrate that the cleaner collider environment gives a high-purity signal sample. In the nominal setup, the multivariate analysis gives a significance above $5\sigma$ already at $300~{\rm fb}^{-1}$. At integrated luminosities of order $1-3~{\rm ab}^{-1}$, the branching ratio can be measured with several-percent precision.

We address the question of whether dualities formulated in continuum field theory can be realised exactly at finite lattice spacing, rather than only emerging in the infrared. In this context, we construct a lattice framework for a genuinely stringy form of T-duality. We extend the exact lattice T-duality of the compact boson to curved backgrounds with non-trivial circle fibrations, where the duality is no longer exhausted by the familiar exchange of momentum and winding, but also involves global topological data. To this end, we define the twisted Villain model, which couples the lattice fibre field to cochains encoding the bundle connection and the fibre-horizontal component of the $B$-field. We realise this structure in lattice models for several fibred backgrounds and recover the characteristic bundle-flux exchange of T-duality. Using a half-gauging procedure, we derive the associated lattice defect action and show that it defines a topological defect. This establishes that the distinctive topological features of T-duality on curved manifolds can be captured exactly in a lattice model, implying that this duality is not tied to a particular continuum representation is present in lattice-regularised models.

Can a closed quantum system generate persistent time-crystal-like dynamics without external driving? Within the Bateman dual oscillator framework, we show that the answer is affirmative. We consider a nonrelativistic (2+1)-dimensional system in which spin-induced spatial deformation generates an effective Bateman oscillator structure. After quantization, the system is governed by a time-independent Hermitian Hamiltonian describing coherent coupling between damped and amplified oscillator sectors while preserving the total energy of the global doubled system. Tracing over the amplified sector, we derive an effective non-Markovian reduced dynamics for the observable subsystem. The resulting memory effects sustain persistent oscillations of subsystem observables and generate emergent time-crystal-like temporal ordering without external periodic driving or equilibrium spontaneous symmetry breaking. Since the oscillatory behavior originates from nonequilibrium reduced subsystem dynamics rather than equilibrium expectation values of the full Hamiltonian, the mechanism lies outside the assumptions of conventional no-go theorems for equilibrium time crystals. The same dynamics further exhibits logarithmic-spiral trajectories and self-similar fractal scaling, revealing a direct connection between coherent dissipative dynamics, non-Markovian memory effects, and emergent temporal ordering in a globally unitary quantum system. In this specific sense, "watching the growth" of these self-similar structures corresponds to observing the gradual formation of time-crystal-like ordering.

Based on quantum field theory of linearized gravity, we formulate the Wigner function for right- and left-handed gravitons. By applying the Wigner transformation to the second-order metric perturbations in the graviton energy-momentum tensor obtained from the Einstein-Hilbert action, we demonstrate the emergence of the spin Hall effect of gravitons in curved spacetime. This effect originates from the Berry curvature of gravitons, which has opposite signs for right- and left-handed helicities, and leads to a helicity-dependent splitting of the graviton energy Hall current. The magnitude of this splitting is found to be exactly twice that of the corresponding spin Hall current for photons.

We recalculate the contributions of individual six loop graphs to the $\beta$-function for a three dimensional scalar theory with an arbitrary sextic scalar potential. Previously this was calculated by Hager who specialised to a theory with maximal $O(N)$ symmetry. Our results differ in some contributions to the overall $\beta$-function but agree with a recent calculation \cite{Kompaniets2}. At large $N$ three eight loop diagrams which are relevant are calculated. At the $O(N)$ fixed point some critical exponents are determined to $\rm O(\varepsilon^3)$. Imposing that the $\beta$-function satisfies a gradient flow equation is shown to require linear relations between some $\beta$-function coefficients. The curvature for the associated metric is also determined. Detailed results for the Feynman integrals are described in the appendices.

We derive the graviton scattering map in the null-surface formulation (NSF) through third order in perturbations of Minkowski spacetime. The rational structure of the exact NSF equations allows a recursive perturbative construction of the cut function, conformal factor, and geometric sources. At third order, matching future and past null-surface reconstructions determines the cubic correction $\delta a^{\mathrm{out}}_{3,\lambda}$ to the outgoing graviton operators. We then study the connected one-loop contribution from $\delta a^{\mathrm{out}}_3 \delta a^{\mathrm{out}}_3$. Delta functions enforce total three-momentum conservation and reduce internal integrations to a single loop momentum. The ultraviolet scaling is controlled by the radiative mode weight $\nu(\omega)=8\pi^2\sqrt{4\pi G}\,\omega^{-3/2}$. As a result, each normalized vertex scales as $\mathcal{O}(K^{-2})$, yielding a radially convergent UV tail bounded by $\int^\infty dK/K^4$. The plane-wave kernel is therefore radially UV finite, while smooth wave packets define the physical domain of the operator distributions. Finally, the corrections preserve Hermitian conjugation and are compatible order by order with a unitary Baker–Campbell–Hausdorff representation of the asymptotic scattering map.

Within general relativity, black holes are widely regarded as the ultimate benchmark for compactness in the Universe. Recently, however, neutron star models have been constructed in a higher-curvature theory – quasi-topological gravity (QTG) – whose compactness can exceed the black-hole limit~ [S. Li, H. Lü, Y. Gao, R. Xu, L. Shao, and H. Yu, companion Letter, Neutron stars more compact than black holes as a probe of strong-field gravity, Phys. Rev. D 114, L021504 (2026).]. Here we present a detailed analysis of both the equilibrium structure and radial stability of such configurations in QTG. By examining several representative equations of state and different values of the gravitational coupling constant, we find that in the high-central-density regime the compactness exceeding the black-hole bound exhibits a universal behavior in QTG. We further show that QTG corrections grow increasingly significant at large central densities and can stabilize configurations that are radially unstable in general relativity over a broad parameter range. These results establish ultra-compact neutron stars in QTG as theoretically viable strong-field configurations and provide a foundation for further investigations of their dynamical and phenomenological implications.

We study the capacity of entanglement in the microcanonical ensemble for an effectively additive bipartite system. Using typicality and the block structure of the microcanonical reduced state, we show that in the thermodynamic regime the capacity is controlled by energy-sharing fluctuations and can be expressed purely in terms of standard thermal response data of the subsystems. As an illustration, we apply the result to a toy model consisting of a Schwarzian “black-hole” sector coupled to a two-dimensional CFT radiation sector. At fixed total energy, the growth of the radiation sector forces the common temperature to decrease, producing a smooth Page-like single-hump curve for the capacity. We also distinguish the capacity of the reduced microcanonical state from that of a Haar-typical pure state in the same energy shell. A block-Wishart analysis shows that the effective-heat-capacity result holds on both sides of the Page crossover, while a universal folded-normal scaling function resolves a narrow window in which the two effective Hilbert-space dimensions become comparable. The construction is an equilibrium microcanonical mechanism for Page-like capacity curves, rather than a complete dynamical evaporation calculation.

We investigate the finite-time instability of massive spinning test particles around a rotating hairy black hole generated through gravitational decoupling. The particle motion is described by the full Mathisson-Papapetrou-Dixon equations with the Tulczyjew spin supplementary condition, and the sensitivity to initial conditions is measured using a ZAMO-projected finite-time Lyapunov analysis. The hairy deformation is controlled by two parameters: $\alpha$, which sets the deviation from Kerr, and $\beta$, which changes the radial localization of the deformation. We show that spin-curvature coupling and the hairy geometry can shift the evolved orbit away from the requested seed parameters, making the empirical orbital map essential for interpreting the dynamics. Small-spin and geodesic trajectories remain close to regular behavior, whereas large-spin trajectories show stronger finite-time growth. A scan of the $(S,\beta)$ plane shows that the instability does not grow monotonically, but appears in localized regions where the particle spin and the radial profile of the hair act cooperatively. Thus, the hairy background does not simply rescale the Kerr result; it reorganizes the strong-field phase-space region sampled by spinning particles.

An $SO(3)$-gauged Higgs model on $\mathbb{R}^3$ is proposed that, like the Abelian Higgs model on $\mathbb{R}^2$, features both attractive and repulsive phases, though unlike the latter its solutions do not saturate the topological lower bound. What distinguishes this model is that its energy is stabilised by the "Higgs analogue of the Chern-Pontryagin" charge, rather than the usual "Higgs–Chern-Pontryagin" charge which is a dimensional descendant of the Chern-Pontryagin charge.

Exploiting newly available data on Gopakumar-Vafa invariants at high genus for one-parameter hypergeometric Calabi-Yau threefolds, we study numerically the growth of the 5D indices, stable pair (PT) invariants and rank one Donaldson-Thomas (DT) invariants at large charges. For the 5D index $\Omega_{5D}(d,m)$, below a critical value of the angular momentum $m$, we find perfect agreement with the Bekenstein-Hawking-Wald entropy of rotating 5D BMPV black holes, including the subleading correction from four-derivative interactions. When $m$ exceeds the critical value, the 5D index is instead dominated by black rings with the smallest possible dipole charge. The stable pair invariant $PT(d,m)$, which is determined by 5D indices, has a similar black ring/hole transition at negative $m$ (now interpreted as the D0-brane charge) but surprisingly exhibits two other phase transitions at positive $m$: first, to a plateau and then to a polynomial growth $\sim m^{2d-1}$. In each phase, we derive an approximate expression for the invariant. Finally, the rank one DT invariant $DT(d,m)$ is similar to $PT(d,m)$ at negative $m$, and then transitions to a phase dominated by D0-branes, with entropy of order $m^{2/3}$. Along the way, we determine the fixed genus, large degree behavior of GV invariants (including the overall $g$-dependent constant), extend it to an approximate formula valid also for large $g$, point out the unreasonable effectiveness of a simple PT/MSW relation, and study the growth of topological free energies at fixed degree, confirming a conjecture of Mariño.

We construct a surjective homomorphism from the (suitably interpreted) double loop-nilpotent $K$-theoretic Hall algebra to the Coulomb branch algebra of a quiver gauge theory, using the shuffle algebra interpretation.

We study the conjecture that a sum of the (g-1)st powers of adjoint Reidemeister torsions for a torus knot is an integer. We prove that the conjecture is true for any torus knot and all non-negative g. To prove the conjecture, we introduce the Verlinde numbers for torus knots from the viewpoint of modular S-matrix and show the recursion formulas and initial values of them. The recursion formulas of Verlinde numbers prove the integrality of the sum of the (g-1)st powers of adjoint Reidemeister torsions. Related to a modular S-matrix, we also provide a birational model of the character variety for a torus knot and show how to recover the adjoint Reidemeister torsion for a torus knot from the Hessian of the polynomial defining the birational model.

In this work we ask what the self-consistency of a classical hydrodynamic description imposes on a quantum system. The quantum fluctuation-dissipation theorem, when read in the time domain, acts as a blurring of the fine details of the correlation functions on a Plankian time-scale. We track this blurring along rays inside the light cone for three phenomenological hydrodynamic equations – diffusion, telegraph and diffusive-telegraph – and find that the interior of the cone splits into a classical region, where correlation and response satisfy the classical fluctuation-dissipation relation, and a quantum region, where they deviate sharply from it. Preserving a finite classical region as the temperature is lowered forces the effective relaxation rate to be at least Planckian, recovering bounds on diffusivity, equilibration time and shear viscosity. In this way, Planckian scaling of the diffusion constant emerges not as a quantum constraint on microscopic dynamics, but as the price a system pays to remain describable by classical hydrodynamics down to low temperatures.

We construct a family of non-invertible topological defects in two-dimensional theories of $n$ Weyl fermions. The construction relies on the existence of $G$-symmetric conformal boundary conditions for $n$ Dirac fermions. Upon unfolding, these boundary conditions become topological defects $\mathcal D$ of $n$ Weyl fermions that intertwine the two $G$-representations, and they are generically non-invertible. For $G=U(1)^n$, we show that $\mathcal D$ is a duality defect associated with gauging a finite Abelian group $\Gamma$, and we give an explicit algorithm for determining $\Gamma$ and its action on the fermions. We also show that the same finite-Abelian gauging description applies in certain restricted examples with non-Abelian $G$. By contrast, for certain non-Abelian symmetry structures, including the $G=SU(2)$ symmetry appearing in the $1$-$5$-$7$-$8$-$9$ problem, we prove that $\mathcal D$ cannot be realized as a duality defect for gauging any finite Abelian group. Finally, we explain how the duality-defect perspective gives a streamlined derivation of fermion scattering from a conformal boundary.