arXiv subjects

Arnab Kundu

Publications and source records attributed to Arnab Kundu.

At least 55 records · Page 3Linked to original sources

arXiv2021

Semi-equivelar toroidal maps and their k-edge covers

If the face\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\mbox{-}equivelar. A tiling is edge-homogeneous if any two edges with vertices of congruent face-cycles. In general, edge-homogeneous maps on a surface form a bigger class than edge-transitive maps. There are edge-homogeneous toroidal maps which are not edge\mbox{-}transitive. An edge-homogeneous map is called $k$-edge-homogeneous if it contains $k$ number of edge orbits. In particular, if $k=1$ then it is called edge-transitive map. In general, a map is called $k$-edge orbital or $k$-orbital if it contains $k$ number of edge orbits. A map is called minimal if the number of edges is minimal. A surjective mapping $η\colon M \to K$ from a map $M$ to a map $K$ is called a covering if it preserves adjacency and sends vertices, edges, faces of $M$ to vertices, edges, faces of $K$ respectively. Orbani{\' c} et al. and {\v S}ir{á}{\v n} et al. have shown that every edge-homogeneous toroidal map has edge-transitive cover. In this article, we show the bounds of edge orbits of edge-homogeneous toroidal maps. Using these bounds, we show the bounds of edge orbits of non-edge-homogeneous semi-equivelar toroidal maps. We also prove that if a edge-homogeneous map is $k$ edge orbital then it has a finite index $m$-edge orbital minimal cover for $m \le k$. We also show the existence and classification of $n$ sheeted covers of edge-homogeneous toroidal maps for each $n \in \mathbb{N}$. We extend this to non-edge-homogeneous semi-equivelar toroidal maps and prove the same results, i.e., if a non-edge-homogeneous map is $k$ edge orbital then it has a finite index $m$-edge orbital minimal cover (non-edge-homogeneous) for $m \le k$ and then classify them for each sheet.

math.CO↗

arXiv2021

Tilting Correspondences of Perfectoid Rings

In this article, we present an alternate proof of a vanishing result of étale cohomology on perfectoid rings due to Česnavičius and more recently proved by a different approach by Bhatt and Scholze. To establish that, we prove a tilting equivalence of étale cohomology of perfectoid rings taking values in commutative, finite étale group schemes. On the way, we algebraically establish an analogue of the tilting correspondences of Scholze, between the category of finite étale schemes over a perfectoid ring and that over its tilt, without using tools from almost ring theory or adic spaces.

math.AG↗

arXiv2021

Critical Quenches, OTOCs and Early-Time Chaos

In this article, we explore dynamical aspects of Out-of-Time-Order correlators (OTOCs) for critical quenches, in which an initial non-trivial state evolves with a CFT-Hamiltonian. At sufficiently large time, global critical quenches exhibit a universal thermal-behaviour in terms of low-point correlators. We demonstrate that, under such a quench, OTOCs demarcate chaotic CFTs from integrable CFTs by exhibiting a characteristic exponential Lyapunov growth for the former. Upon perturbatively introducing inhomogeneity to the global quench, we further argue and demonstrate with an example that, such a perturbation parameter can induce a parametrically large scrambling time, even for a CFT with an order one central charge. This feature may be relevant in designing measurement protocols for non-trivial OTOCs, in general. Both our global and inhomogeneous quench results bode well for an upper bound on the corresponding Lyapunov exponent, that may hold outside thermal equilibrium.

hep-th↗

arXiv2021

Warped Information and Entanglement Islands in AdS/WCFT

We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT$_2$ degrees of freedom. In agreement with the literature, we find entanglement islands and a phase transition in the entanglement surface, but our results differ significantly from work in AdS/CFT in three major ways: (1) the late-time entropy decreases in time, (2) island degrees of freedom exist at all times, and not just at late times, with the phase transition changing whether or not these degrees of freedom include the black hole interior, and (3) the physics involves a field-theoretic IR divergence, emerging when the boundary interval is too big relative to the black hole's inverse temperature. This behavior in the entropy appears to be consistent with the non-unitarity of holographic warped CFT$_2$ and demonstrates that the islands are not a phenomenon restricted to black hole information in unitary setups.

hep-th↗

arXiv2021

Chaotic Correlation Functions with Complex Fermions

We study correlation functions in the complex fermion SYK model. We focus, specifically, on the h = 2 mode which explicitly breaks conformal invariance and exhibits the chaotic behaviour. We explicitly compute fermion six-point function and extract the corresponding six-point OTOC which exhibits an exponential growth with maximal chaos. Following the program of Gross-Rosenhaus, this correlator contains information of the bulk cubic coupling, at the conformal point as well as perturbatively away from it. Unlike the conformal modes with high values of h, the h = 2 mode has contact interaction dominating over the planar in the large q limit.

hep-th↗

arXiv2020

Fast Scrambling under an RG-flow

The notion of information scrambling is tied to the long-time behaviour of a system and therefore is related to its infra-red dynamics. In fast scramblers, information spreads as a logarithmic function of the number of degrees of freedom. Ordinarily, under an RG-flow, scrambling will become faster in the IR since many degrees of freedom are integrated out, as a consequence of the c-theorem. In this article, we consider a class of Holographic quantum field theories (QFT), which are strongly coupled large $N$ gauge theories with large number of adjoint and fundamental matter, in which scrambling slows down in the IR. This happens since more degrees of freedom are inserted in the IR, compared to the UV, in a precise sense. For generic large $N$ gauge theories, we also explore general, perturbative flow features of the corresponding Lyapunov exponent, based on the Callan-Symanzik equation.

hep-th↗

arXiv2020

Rotating Black Holes in AdS, Extremality and Chaos

Extremal black holes have vanishing Hawking temperatures. In this article, we argue that for asymptotically AdS black holes, at extremality, a particular class of correlators in the dual CFT can exhibit exponential, maximally chaotic growth with a non-vanishing temperature. Our approach, at extremality, is two-fold. First, we geometrically investigate the modes that are responsible for chaos. Secondly, we study the dynamics of a probe string to capture chaos in worldsheet correlators. For rotating BTZ at extremality, the corresponding Lyapunov exponent is determined by the left-moving temperature. In higher dimensional AdS-Kerr geometries, on the other hand, the corresponding Lyapunov exponent becomes a non-trivial function of the Frolov-Thorne temperatures.

hep-th↗

arXiv2020

Verification of a Generative Separation Kernel

We present a formal verification of the functional correctness of the Muen Separation Kernel. Muen is representative of the class of modern separation kernels that leverage hardware virtualization support, and are generative in nature in that they generate a specialized kernel for each system configuration. These features pose substantial challenges to existing verification techniques. We propose a verification framework called conditional parametric refinement which allows us to formally reason about generative systems. We use this framework to carry out a conditional refinement-based proof of correctness of the Muen kernel generator. Our analysis of several system configurations shows that our technique is effective in producing mechanized proofs of correctness, and also in identifying issues that may compromise the separation property.

cs.PL↗

arXiv2020

A Killing Vector Treatment of Multiboundary Wormholes

The two-sided BTZ black hole has been instrumental in elucidating several aspects of AdS/CFT. Similarly, multiboundary wormholes provide a useful and rich arena in which probing questions of quantum gravity can be posed and explored. In this work, we find the explicit forms of the Killing vectors needed to construct three-boundary wormholes, with and without rotation, as quotients of AdS$_3$. We ensure that our method captures the full moduli space of such wormholes and elaborate on the generalization of our procedure to more exotic multiboundary spaces, including higher genus.

hep-th↗

arXiv2019

Real Time Dynamics in Low Point Correlators in 2d BCFT

In this article, we demonstrate how a 3-point correlation function can capture the out-of-time-ordered features of a higher point correlation function, in the context of a conformal field theory (CFT) with a boundary, in two dimensions. Our general analyses of the analytic structures are independent of the details of the CFT and the operators, however, to demonstrate a Lyapunov growth we focus on the Virasoro identity block in large-c CFT's. Motivated by this, we also show that the phenomenon of pole-skipping is present in a 2-point correlation function in a two-dimensional CFT with a boundary. This pole-skipping is related, by an analytic continuation, to the maximal Lyapunov exponent for maximally chaotic systems. Our results hint that, the dynamical content of higher point correlation functions, in certain cases, may be encrypted within low-point correlation functions, and analytic properties thereof.

hep-th↗

arXiv2018

Effective Thermal Physics in Holography: A Brief Review

It is well-known that a Rindler observer measures a non-trivial energy flux, resulting in a thermal description in an otherwise Minkowski vacuum. For systems consisting of large number of degrees of freedom, it is natural to isolate a small subset of them, and engineer a steady state configuration in which these degrees of freedom act as Rindler observers. In Holography, this idea has been explored in various contexts, specifically in exploring the strongly coupled dynamics of a fundamental matter sector, in the background of adjoint matters. In this article, we briefly review some features of this physics, ranging from the basic description of such configurations in terms of strings and branes, to observable effects of this effective thermal description.

hep-th↗

arXiv2018

Maximal Chaos from Strings, Branes and Schwarzian Action

In this article, we explicitly demonstrate that, for a sufficiently generic class of examples, an open string embedded in an AdS-background yields an effective Schwarzian action and, in the semi-classical description, the fluctuation modes of the open string couple to this Schwarzian sector. This leads to a maximal chaos, observed in the open string degrees of freedom, irrespective of the gravitational background. This corresponds to the dynamics of quark-like degrees of freedom in a strongly coupled large N_c gauge theory. We also demonstrate a maximal chaos, resulting from an inherent D-brane horizon, by computing the four-point out-of-time-ordered correlator of spin-one operators. We also offer some observations and comments regarding a class of effective theories that is described by a generic functional of a Schwarzian derivative.

hep-th↗

arXiv2018

Strings, Branes, Schwarzian Action and Maximal Chaos

In this article, we present explicit evidence that maximal chaos occurs for a generic, probe quark-like defect degrees of freedom, in a strongly coupled large $N_c$ gauge theory. In holography, this corresponds to the dynamics of open string degrees of freedom, in the background of a closed string geometry. In this context, we explicitly show that a Schwarzian effective action for the soft sector emerges and couples with other modes, in the infra-red. This is manifest on an open string worldsheet, as well as a D$1$-brane world-volume, embedded in AdS$_3$. The corresponding maximal chaos is governed by an intrinsic defect D-brane horizon, and an intrinsic non-linear description of the brane or the string. We also present explicit evidence of maximal chaos away from extremality on a D-brane horizon, by computing a four-point out-of-time order correlator of spin-one operators. This further suggests that a similar description of the soft sector physics of open string degrees of freedom may exist in general.

hep-th↗

arXiv2018

Scale invariance with fundamental matters and anomaly: A holographic description

Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field theory with large and arbitrary number of adjoint and fundamental degrees of freedom and a non-vanishing chiral anomaly, in the presence of an external magnetic field and with a non-vanishing density. Motivated by the richness of quantum chromodynamics under similar condition, we explore the solution space to find an infinite class of scale-invariant, but not conformal, field theories that may play a pivotal role in defining the corresponding physics. In particular, we find two classes of geometries: Schrodinger isometric and warped AdS_3 geometries with an SL(2,R) X U(1) isometry. We find hints of spontaneous breaking of translational symmetry, at low temperatures, around the warped backgrounds.

hep-th↗

arXiv2017

Fundamental Flavours, Fields and Fixed Points: A Brief Account

In this article we report on a preliminary study, {\it via} Holography, of infrared fixed points in a putative strongly coupled SU$(N_c)$ gauge theory, with $N_f$ fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently {\it effective} or a {\it bottom up} approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: AdS$_m \times {\mathbb R}^n$--type, and AdS$_m \times$EAdS$_n$--type, where $m$ and $n$ are suitable integers. Both these classes of solutions are {\it non-perturbative} in back-reaction. The AdS$_m \times$EAdS$_n$--type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS$_5$ ultraviolet to both an AdS$_2$ and an AdS$_3$ IR.

hep-th↗

arXiv2017

SYK Model, Chaos and Conserved Charge

We study the SYK model with complex fermions, in the presence of an all-to-all $q$-body interaction, with a non-vanishing chemical potential. We find that, in the large $q$ limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential $μ$. Even when the coupling $J$, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of $μ$ which are exponentially small compared to $J$ lead to suppression of the Lyapunov exponent.

hep-th↗

arXiv2017

Flavours and Infra-red Instability in Holography

Within a phenomenological holographic model in $(4+1)$-bulk dimensions, defined by Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld and a Chern-Simons term, we explore the fate of BF-bound violation for a probe scalar field and a fluctuation mode of the corresponding geometry. We assume this simple model to capture the dynamics of a strongly coupled SU$(N_c)$ gauge theory with $N_f$ fundamental matter, which in the limit ${\cal O} \left( N_c \right) \sim {\cal O}\left(N_f\right)$ and with a non-vanishing matter density, is holographically described by an AdS$_2$-geometry in the IR. We demonstrate that, superconductor/superfluid instabilities are facilitated and spontaneous breaking of translational invariance is inhibited with increasing values of $\left(N_f / N_c \right) $. This is similar, in spirit, with known results in large $N_c$ Quantum Chromodynamics with $N_f$ quarks and a non-vanishing density, in which the chiral density wave phase becomes suppressed and superconducting instabilities become favoured as the number of quarks is increased.

hep-th↗

arXiv2017

Oscillating Shells and Oscillating Balls in AdS

It has recently been reported that certain thin timelike shells undergo oscillatory motion in AdS. In this paper, we compute two-point function of a probe field in the geodesic approximation in such an oscillating shell background. We confirm that the two-point function exhibits an oscillatory behaviour following the motion of the shell. We show that similar oscillatory dynamics is possible when the perfect fluid on the shell has a polytropic equation of state. Moreover, we show that certain ball like configurations in AdS also exhibit oscillatory motion and comment on how such a solution can be smoothly matched to an appropriate exterior solution. We also demonstrate that the weak energy condition is satisfied for these oscillatory configurations.

hep-th↗