arXiv subjects

Arnab Kundu

Publications and source records attributed to Arnab Kundu.

At least 19 recordsLinked to original sources

arXiv2026

Fixed Points, Floquet Entanglement Asymmetry, and Quantum Mpemba Effects

We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U$(1)$ symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.

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arXiv2026

Non-relativistic Floquet Conformal Field Theory

We develop a formalism for studying Floquet dynamics for systems with non-relativistic conformal invariance in d spatial dimensions. Our analysis indicates the existence of two dynamical phases, hyperbolic and elliptic, separated by a parabolic transition surface. We demonstrate this by studying the fidelity of the driven state and the expectation value of a conformal generator in the many body ground state during the drive. Stroboscopically, they behave exponentially in the hyperbolic phase, show oscillatory behavior in the elliptic phase, and exhibit power-law on the transition surface. Our analysis is completely universal and can be directly applied to several systems including trapped fermions near unitarity and resonant anyons. The former can provide experimental signatures of these dynamical phases. We also comment on a holographic perspective of such driven non-relativistic CFTs and demonstrate that the hyperbolic phase is associated with a timelike stationary-limit surface, such as an ergosphere, in the bulk, while the parabolic phase corresponds to an extremal Killing horizon.

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arXiv2026

$\mathbb{A}^1$-connectivity of motivic spaces

We prove a version of Morel's unstable $\mathbb{A}^1$-connectivity theorem over arbitrary base schemes. In the stable setting, this recovers (and simplifies the proof of) the known connectivity bounds due to Morel, Schmidt--Strunk, Deshmukh--Hogadi--Kulkarni--Yadav, and Druzhinin, and extends them to possibly non-noetherian schemes. Using the recent work of Bachmann--Elmanto--Morrow, this also implies that the slice filtration on homotopy $K$-theory is convergent for qcqs schemes of finite valuative dimension.

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arXiv2026

Beilinson--Lichtenbaum phenomenon for motivic cohomology

The goal of this paper is to study non-$\mathbb{A}^1$-invariant motivic cohomology, recently defined by Elmanto, Morrow, and the first-named author, for smooth schemes over possibly non-discrete valuation rings. We establish that the cycle class map from $p$-adic motivic cohomology to a suitable truncation of Bhatt--Lurie's syntomic cohomology is an isomorphism, thereby verifying the Beilinson--Lichtenbaum conjecture in this generality. As a first consequence, we prove that this motivic cohomology integrally recovers the classical definition of motivic cohomology in terms of Bloch's cycle complexes, whenever the latter is defined. As a second consequence, we show a purity theorem for this cohomology theory over perfectoid rings, thus motivically refining a result of Nizioł in algebraic $K$-theory. The key ingredient in our approach is a version of Gabber's presentation lemma applicable in mixed characteristic, non-noetherian settings.

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arXiv2026

Flat Cohomological Purity for Syntomic Schemes over Valuation Rings

Grothendieck's cohomological purity predicts that the cohomology of a scheme is insensitive to removing a closed subscheme of sufficiently high codimension. In this article, we establish a form of flat cohomological purity over arbitrary (possibly infinite-rank) mixed-characteristic valuation rings $V$, thereby extending the theorem of Česnavičius--Scholze to the non-noetherian setting. More precisely, for a flat finite-type scheme over $V$ with local complete intersection fibres, we prove that the cohomology with coefficients in a commutative finite locally free group scheme remains unchanged after removing a closed subscheme satisfying a suitable fibrewise codimension condition; in particular, we obtain vanishing in low degrees and injectivity in the critical degree. As applications, we deduce purity results for local cohomology, for torsion in the Picard group, and for the Brauer group. In higher rank, our results yield sharper bounds than those previously obtained by Bhatt--Lurie and Madapusi--Mondal. The argument rests on recent advances in the structure theory of valuation rings.

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arXiv2026

Symmetry Resolved Entanglement Entropy: Equipartition under Driven and Non-unitary Evolution in a Compact Boson CFT

We study the evolution of symmetry-resolved entanglement entropy in bulk-driven Floquet conformal field theories (CFTs). Focusing on the two-dimensional free compact boson CFT, we analyze how symmetry-resolved Rényi entropies approach or depart from equipartition among charge sectors. We show that the existence of an $\mathfrak{sl}^{(k)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra introduces a free parameter, the label $k$, which allows us to control the breakdown of equipartition. We argue that this effect originates from an explicit coupling between low- and high-frequency modes. Based on a general oscillator representation of the Virasoro algebra, we expect this mechanism to persist beyond the free boson CFT. Finally, we discuss how the real-time dynamics of fine-grained symmetry-resolved entropies of a boundary state are modified under non-unitary evolution, which can be associated with post-selected weak measurements.

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arXiv2026

Reductification of parahoric group schemes

Parahoric group schemes are certain possibly non-reductive, smooth, affine integral models of reductive group schemes defined over a henselian discretely valued field $K$ whose residue field is perfect. We show that any such group scheme $\mathscr{P}$ becomes reductive, in a particular regard, after a (possibly wildly ramified) finite Galois extension $L/K$. More precisely, we prove that there exists a reductive integral model $\mathscr{G}$ of the base change $\mathscr{P}_L$ such that $\mathscr{P}$ can be recovered as the smoothening of the subgroup of Galois invariants of the Weil restriction of $\mathscr{G}$. Our work extends results of Balaji--Seshadri and Pappas--Rapoport from the tamely ramified and simply-connected semisimple setting. As an application, we establish a parahoric analogue of the Grothendieck--Serre conjecture in sufficiently good residue characteristics. Specifically, we confirm that generically trivial parahoric torsors are trivial whenever the generic reductive group is simply-connected. The proof proceeds by reducing the problem to a statement about a stacky reductive group over a stacky discrete valuation ring.

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arXiv2026

Dynamical Phases of Higher Dimensional Floquet CFTs

This paper investigates the dynamical phases of Floquet Conformal Field Theories (CFTs) in space-time dimensions greater than two. Building upon our previous work [1] which introduced quaternionic representations for studying Floquet dynamics in higher dimensional CFTs, we now explore more general square pulse drive protocols that go beyond a single SU(1,1) subgroup. We demonstrate that, for multi-step drive protocols, the system exhibits distinct dynamical phases characterized by the nature of the eigenvalues of the quaternionic matrix representing time evolution in a single cycle, leading to different stroboscopic responses. Our analysis establishes a fundamental geometric interpretation where these dynamical phases directly correspond to the presence or absence of Killing horizons in the base space of the CFT and in a higher dimensional AdS space on which a putative dual lives. The heating phase is associated with a non-extremal horizon, the critical phase with an extremal horizon which disappears in the non-heating phase. We develop perturbative approaches to compute the Floquet Hamiltonians in different regimes and show, how tuning drive parameters can lead to horizons, providing a geometric framework for understanding heating phenomena in driven conformal systems.

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arXiv2026

Timelike Entanglement Signatures of Ergodicity and Spectral Chaos

We investigate timelike entanglement measures derived from the spacetime density kernel in the Rosenzweig-Porter model and show that they sharply diagnose both eigenvector ergodicity and spectral chaos. For several Hilbert-space bipartitions, we compute the second Tsallis entropy, the entanglement imagitivity that quantifies non-Hermiticity, and Schatten-norm diagnostics of the kernel. The imagitivity and Frobenius norm exhibit rapid growth and high late-time plateaus in the ergodic regime, are suppressed in the localized regime, and show intermediate behavior in the fractal phase. The real part of the second Tsallis entropy displays a spectral form factor-like dip-ramp-plateau throughout the chaotic window and a suppressed ramp in the localized regime. We further introduce a kernel negativity, defined as the negative spectral weight of the Hermitian part of the kernel. This negativity equals the trace-norm distance to the set of positive semidefinite operators and the maximal witnessable negative quasiprobability, and its time-averaged value decreases across the ergodic-fractal-localized crossover in close correspondence with the fractal dimension.

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arXiv2025

Temporal correlations and chaos from spacetime kernel

We develop a finite-dimensional formulation of the recently introduced notion of ``timelike entanglement'', defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator basis, we recast this construction in terms of a generalized response tensor. Building on this, we introduce a generalized spacetime density kernel (GSDK) corresponding to higher-point correlation functions, including time-ordered as well as out-of-time-ordered correlators. We show that the Haar-averaged $(2N)$-point function yields the $(2N)$-th moment of the spectral form factor (SFF), evaluated at an $N$-enhanced effective temperature. The correlation functions of the GSDK operators also yield the SFF, with an effective $(1/N)$-reduction of the physical time-scales. The GSDK places both scrambling diagnostics and spectral statistics on a similar footing and clarifies how higher-point correlators and non-trivial time ordering capture fine-grained dynamical information of a quantum system.

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arXiv2025

Blackish Holes with Stringy Backreaction

Recent studies have demonstrated that an $\textit{ad hoc}$ Dirichlet boundary condition, placed outside but close to an event horizon, for probe degrees of freedom in an otherwise black hole geometry is capable of capturing non-trivial level-correlations of the corresponding spectrum of the probe sector. Much of the interesting physics stems from a hierarchy of scales that is present in the quantum spectrum, in terms of two quantum numbers that characterize it. In this work, we establish an explicit connection with the hierarchy of these scales with a $\textit{radial localization}$ or the absence of it of the probe scalar WKB-wavefunction. Subsequently, this scale separation can be traced back to the hierarchy between the local red-shift and the classical light-traversing time in a geometry that produces a Rindler-throat. The classical null ray takes a logarithmically divergent time to reach the Dirichlet wall, and interestingly, we explicitly demonstrate that the scalar quantum spectrum arising from the Rindler throat yields a Dip-time of the corresponding spectral form factor, which scales with a universal power of the light traversing time. Armed with these, we further consider a $\textit{dressed effective model}$ where the Dirichlet boundary condition is inserted in a ten-dimensional supergravity geometry, where classical string sources back-react. We demonstrate that, as a result of this backreaction, the quantum-dynamical time-scales, $\textit{e.g.}$ the Dip time of the corresponding spectral form factor can be further enhanced with factors of the string length, thereby making the Dirichlet wall configuration better mimic the true black hole. In the dual field theory, the geometry corresponds to thermal states of a large $N$ gauge theory in the Veneziano limit, where both the number of colour and the flavour degrees of freedom are large.

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arXiv2025

Isotropic Torsors on Smooth Algebras over Prüfer Rings

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of Česnavičius and Fedorov, we prove a non-noetherian analogue of this conjecture for rings $A$ that are semilocalisations of smooth schemes over valuation rings of rank one, and for reductive $A$-group schemes $G$ that are totally isotropic. Roughly speaking, such group schemes are characterised by the existence of a parabolic subgroup of their adjoint quotients. Since quasi-split groups are totally isotropic, our result, in particular, generalises the Grothendieck--Serre result of Guo--Liu and the author's thesis. Our proof relies on a new instance of Gabber's presentation lemma, obtained by extending techniques developed in the author's thesis.

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arXiv2025

Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity

We investigate quantum chaotic features of the brickwall model, which is obtained by introducing a stretched horizon - a Dirichlet wall placed outside the event horizon - within the BTZ geometry. This simple yet effective model has been shown to capture key properties of quantum black holes and is motivated by the stringy fuzzball proposal. We analyze the dynamics of both scalar and fermionic probe fields, deriving their normal mode spectra with Gaussian-distributed boundary conditions on the stretched horizon. By interpreting these normal modes as energy eigenvalues, we examine spectral statistics, including level spacing distributions, the spectral form factor, and Krylov state complexity as diagnostics for quantum chaos. Our results show that the brickwall model exhibits features consistent with random matrix theory across various ensembles as the standard deviation of the Gaussian distribution is varied. Specifically, we observe Wigner-Dyson distributions, a linear ramp in the spectral form factor, and a characteristic peak in Krylov complexity, all without the need for a classical interior geometry. We also demonstrate that non-vanishing spectral rigidity alone is sufficient to produce a peak in Krylov complexity, without requiring Wigner-Dyson level repulsion. Finally, we identify signatures of integrability at extreme values of the Dirichlet boundary condition parameter.

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arXiv2025

Flowery Horizons & Bulk Observers: $sl^{(q)}(2,\mathbb{R})$ Drive in $2d$ Holographic CFT

We explore and analyze bulk geometric aspects corresponding to a driven two-dimensional holographic CFT, where the drive Hamiltonian is constructed from the $sl^{(q)}(2,\mathbb{R})$ generators. In particular, we demonstrate that starting with a thermal initial state, the evolution of the event horizon is characterized by distinct geometric transformations in the bulk which are associated to the conjugacy classes of the corresponding transformations on the CFT. Namely, the bulk evolution of the horizon is geometrically classified into an oscillatory (non-heating) behaviour, an exponentially growing (heating) behaviour and a power-law growth with an angular rotation (the phase boundary), all as a function of the stroboscopic time. We also show that the explicit symmetry breaking of the drive is manifest in a flowery structure of the event horizon that displays a $U(1) \to {\mathbb Z}_q$ symmetry breaking. In the $q\to \infty$ limit, the $U(1)$ symmetry is effectively restored. Furthermore, by analyzing the integral curves generated by the asymptotic Killing vectors, we also demonstrate how the fixed points of these curves approximate a bulk Ryu-Takayanagi surface corresponding to a modular Hamiltonian for a sub-region in the CFT. Since the CFT modular Hamiltonian has an infinitely many in-equivalent extensions in the bulk, the fixed points of the integral curves can also lie outside the entanglement wedge of the CFT sub-region.

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arXiv2025

Blackish Holes

Based on previous works, in this article we systematically analyze the implications of the explicit normal modes of a probe scalar sector in a BTZ background with a Dirichlet wall, in an asymptotically AdS-background. This is a Fuzzball-inspired geometric model, at least in an effective sense. We demonstrate explicitly that in the limit when the Dirichlet wall approaches the event horizon, the normal modes condense fast to yield an effective branch cut along the real line in the complex frequency plane. In turn, in this approximation, quasi-normal modes associated to the BTZ black hole emerge and the corresponding two-point function is described by a thermal correlator, associated with the Hawking temperature in the general case and with the right-moving temperature in the extremal limit. We further show, analytically, that the presence of a non-vanishing angular momentum non-perturbatively enhances this condensation. The consequences are manifold: {\it e.g.}~there is an emergent {\it strong thermalization} due to these modes, adding further support to a quantum chaotic nature associated to the spectral form factor. We explicitly demonstrate, by considering a classical collapsing geometry, that the one-loop scalar determinant naturally inherits a Dirichlet boundary condition, as the shell approaches the scale of the event horizon. This provides a plausible dynamical mechanism in the dual CFT through a global quench, that can create an emergent Dirichlet boundary close to the horizon-scale. We offer comments on how this simple model can describe salient features of Fuzzball-geometries, as well as of extremely compact objects. This also provides an explicit realization of how an effective thermal physics emerges from a non-thermal microscopic description, within a semi-classical account of gravity, augmented with an appropriate boundary condition.

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arXiv2024

Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two

We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d > 1, whose quench and Floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for which Hamiltonian evolution takes place with different deformations of the original CFT Hamiltonian in successive time intervals. These deformations are realized by specific combinations of conformal generators with a deformation parameter $β$; the $β< 1$ ($β> 1$) Hamiltonians can be unitarily related to the standard (Luscher-Mack) CFT Hamiltonian. The resulting time evolution can be then calculated by conformal transformations. For $d\leq 3$ we show that the transformations can be obtained in a quaternion formalism. Evolution with such a single Hamiltonian yields qualitatively different time dependences of observables depending on the value of $β$, ranging from exponential decays characteristic of heating to oscillations and power law decays. This manifests in the behavior of the fidelity, unequal-time correlator, and the energy density at the end of a single cycle of a square pulse protocol with different hamiltonians in successive time intervals. When the Hamiltonians in a cycle involve generators of a single SU(1, 1) subalgebra we calculate the Floquet Hamiltonian. We show that one can get dynamical phase transitions by varying the time period of a cycle, where the system can go from a non-heating phase which is oscillatory as a function of the time period to a heating phase with an exponentially damped behavior. Our methods can be generalized to other discrete and continuous protocols. We also point out that our results are expected to hold for a broader class of QFTs that possesses an SL(2, C) symmetry with fields that transform as quasi-primaries under this. As an example, we briefly comment on celestial CFTs in this context.

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arXiv2024

Moving Mirrors, OTOCs and Scrambling

We explore the physics of scrambling in the moving mirror models, in which a two-dimensional CFT is subjected to a time-dependent boundary condition. It is well-known that by choosing an appropriate mirror profile, one can model quantum aspects of black holes in two-dimensions, ranging from Hawking radiation in an eternal black hole (for an "escaping mirror") to the recent realization of Page curve in evaporating black holes (for a "kink mirror"). We explore a class of OTOCs in the presence of such a boundary and explicitly demonstrate the following primary aspects: First, we show that the dynamical CFT data directly affect an OTOC and maximally chaotic scrambling occurs for the escaping mirror for a large-$c$ CFT with identity block dominance. We further show that the exponential growth of OTOC associated with the physics of scrambling yields a power-law growth in the model for evaporating black holes which demonstrates a unitary dynamics in terms of a Page curve. We also demonstrate that, by tuning a parameter, one can naturally interpolate between an exponential growth associated to scrambling and a power-law growth in unitary dynamics. Our work explicitly exhibits the role of higher-point functions in CFT dynamics as well as the distinction between scrambling and Page curve. We also discuss several future possibilities based on this class of models.

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arXiv2024

Gersten's Injectivity for Smooth Algebras over Valuation Rings

Gersten's injectivity conjecture for a functor $F$ of ``motivic type'', predicts that given a semilocal, ``non-singular'', integral domain $R$ with a fraction field $K$, the restriction morphism induces an injection of $F(R)$ inside $F(K)$. We prove two new cases of this conjecture for smooth algebras over valuation rings. Namely, we show that the higher algebraic $K$-groups of a semilocal, integral domain that is an essentially smooth algebra over an equicharacteristic valuation ring inject inside the same of its fraction field. Secondly, we show that Gersten's injectivity is true for smooth algebras over, possibly of mixed-characteristic, valuation rings in the case of torsors under tori and also in the case of the Brauer group.

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