arXiv subjects

Suchetan Das

Publications and source records attributed to Suchetan Das.

At least 19 recordsLinked to original sources

arXiv2026

Modular quantization and black holes

Witten recently proposed a background-independent algebraic framework for quantum gravity, wherein an observer endowed with a Hamiltonian defines a diffeomorphism invariant worldline algebra manifested by the modified Hamiltonian constraint. In the semiclassical limit, this construction admits a lift to a von Neumann algebra acting on a Hilbert space defined by geodesic in a fixed background. Motivated by this, we revisit quantization of certain class of deformed CFT Hamiltonian on a cylinder to capture non-perturbative aspects of black holes. We construct a type-I Von-Neuman algebra by imposing conformal boundary conditions on cut-offs near fixed points of Hamiltonian flow, acting on a GNS Hilbert space built from highest-weight representation of `emergent modular Virasoro algebra'. Upon identifying the Hamiltonian with the modular Hamiltonian of a sharp subregion associated to a fixed reference KMS (vacuum) state, the algebra changes to type-III$_{1}$ factor. We also discuss the structure of emergent Hilbert spaces using `open-closed string' duality after incorporating an emergent non-trivial center made out of scalars at fixed points. We further employ this modular quantization of a single holographic CFT to demonstrate how the boundary limit of exact Hartle-Hawking correlator of smooth BTZ background emerge in the strict semiclassical limit in an alternative dual description, while at finite $G_{N}$, the corresponding description is intrinsically non-smooth, featuring both a stretched horizon and a boundary cutoff. The exact correlator has also been precisely reproduced from the vacuum correlators in modular quantization. We further discuss the effect of incorporating gravity by including the center via AdS/CFT on boundary correlators, for which the description of a smooth horizon is replaced by a (stretched) horizon containing explicit microstructures embedded within it.

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arXiv2025

Two dimensional de-Sitter and deformed CFTs

We present an alternative dimensional reduction that yields an effective theory of dilatons in a two-dimensional de Sitter background. Specifically, by performing an S-wave reduction of higher-dimensional Einstein gravity, we obtain free massless dilatons in the Nariai static patch, and a dynamically evolving dilatons in the past Milne wedge. We then propose a (Nariai) static patch worldsheet formulation in terms of CFTs with SL(2,$\mathbb{R}$) deformed Hamiltonians on the cylinder. A key feature of this construction is that a stretched horizon in the (Nariai) static patch, equipped with an emergent UV boundary condition, acts as a gravitating observer. Using the similar reduction, we have also obtained a Schwarzian action coupled to free massless dilatons in the near horizon near extremal limit of four dimensional charged AdS black holes. The worldsheet description for the same has been proposed and discussed in \cite{Das:2025cuq}. We also comment on how different notions of worldsheet time may themselves be \textit{emergent}.

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arXiv2025

JT gravity and deformed CFTs

We propose alternative \textit{UV completion} of pure JT gravity as well as CFT coupled to JT gravity, via a class of \textit{deformed} 2D CFT. In AdS/CFT with a prescribed classical limit, pure JT gravity in \textit{one-sided} AdS$_{2}$ black hole is argued to be described by certain holographic deformed CFT on a strip. Equivalently, these deformed CFTs can be recast as CFTs on one-sided AdS$_{2}$ black hole with \textit{emergent conformal boundary condition on a stretched horizon}$-$providing a \textit{proper UV frame} of JT gravity. On the other hand, JT gravity coupled to CFT with fixed central charge of $\mathcal{O}(1)$, is also described by deformed CFT on strip satisfying conformal boundary condition, with a different classical limit. The resulting CFT Hilbert spaces in both of the above classical limits yield the black hole entropy as thermal entropy and the high-energy density of states match that of JT gravity with a precise energy scale correspondence. Moreover, the Hilbert space defined for a two-sided black hole factorizes into two one-sided sectors in both limits. Notably in the second limit, degenerate zero modes of the deformed Hamiltonian$-$characterized by conformal primaries localized at the horizon$-$appear as a residual effect of the stretched horizon boundary condition. Exploiting the second limit, we compute entanglement entropy in one-dimensional quantum systems dual to a conformally glued black hole$-$Poincaré geometry in JT gravity, reproducing a `Page curve' via the quantum extremal surface prescription, with `Page time' set by the stretched horizon cutoff.

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arXiv2025

Entanglement asymmetry in periodically driven quantum systems

We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, $ΔS$, as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of $ΔS$ for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for $m$ cycles of a periodic drive with time period $T$, $ΔS \sim \ln mT$ [$\ln (\ln mT)$] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, $ΔS$ displays small amplitude oscillations around it's initial value as a function of $mT$. We provide a phase diagram for the behavior of $ΔS$ for such driven CFTs as a function of the drive frequency and amplitude.

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arXiv2024

Stretched Horizon from Conformal Field Theory

Recently, it has been observed that the Hartle-Hawking correlators, a signature of smooth horizon, can emerge from certain heavy excited state correlators in the (manifestly non-smooth) BTZ stretched horizon background, in the limit when the stretched horizon approaches the real horizon. In this note, we develop a framework of quantizing the CFT modular Hamiltonian, that explains the necessity of introducing a stretched horizon and the emergence of thermal features in the AdS-Rindler and (planar) BTZ backgrounds. In more detail, we quantize vacuum modular Hamiltonian on a spatial segment of $S^{1}$. Unlike radial quantization, (Euclidean) time circles emerge naturally here which can be contracted smoothly to the `fixed points'(end points of the interval) of this quantization thus providing a direct link to thermal physics. To define a Hilbert space with discrete normalizable states and to construct a Virasoro algebra with finite central extension, a natural regulator ($ε$) is needed around the fixed points. Eventually, in the dual description the fixed points correspond to the horizons of AdS-Rindler patch or (planar) BTZ and the cut-off being the stretched horizon. We construct a (Lorentzian) highest weight representation of that Virasoro algebra. We further demonstrate that two point function in a (vacuum) descendant state of the regulated Hilbert space will reproduce thermal answer in $ε\rightarrow 0$ limit which is analogous to the recent observation of emergent thermality in stretched horizon background. We also argue the thermal entropy of this quantization coincides with entanglement entropy of the subregion. Conversely, the microcanonical entropy corresponding to high energy density of states exactly reproduce the BTZ entropy. Quite remarkably, all these dominant high lying microstates are defined only at finite $ε$ in the regulated Hilbert space.

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arXiv2024

Notes on heating phase dynamics in Floquet CFTs and Modular quantization

In this article, we explore the connection between the heating phase of periodically driven CFTs and the Modular Hamiltonian of a subregion in the vacuum state. We show that the heating phase Hamiltonian corresponds to the Modular Hamiltonian, with the fixed points mapping to the endpoints of the subregion. In the bulk dual, we find that these fixed points correspond to the Ryu-Takayanagi surface of the AdS-Rindler wedge. Consequently, the entanglement entropy associated to the boundary interval within two fixed points exactly matches with the Rindler entropy of AdS-Rindler. We observe the emergent Virasoro algebra in the boundary quantization of the Modular Hamiltonian has a striking similarity with the emergent near Horizon Virasoro algebra. This is a consequence of the fact that while obtaining the boundary Virasoro algebra, a cut-off with conformal boundary condition around the fixed point is introduced, which in the bulk is related to a stretched horizon, with an emergent two-dimensional conformal symmetry. We also argue that as one tunes the parameter space of Floquet Hamiltonians to transition from the non-heating to the heating phase the operator algebra type changes from Von Neumann type $I$ to $III_1$ factor, providing a non-equilibrium analogue of the Hawking-Page transition.

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arXiv2024

A Smooth Horizon without a Smooth Horizon

Recent observations on type III algebras in AdS/CFT raise the possibility that smoothness of the black hole horizon is an emergent feature of the large-$N$ limit. In this paper, we present a $bulk$ model for the finite-$N$ mechanism underlying this transition. We quantize a free scalar field on a BTZ black hole with a Planckian stretched horizon placed as a Dirichlet boundary for the field. This is a tractable model for the stretched horizon that does not ignore the angular directions, and it defines a black hole vacuum which has similarities to (but is distinct from) the Boulware state. Using analytic approximations for the normal modes, we first improve upon 't Hooft's brick wall calculation: we are able to match $both$ the entropy and the temperature, $exactly$. Emboldened by this, we compute the boundary Wightman function of the scalar field in a typical pure state built on our stretched horizon vacuum, at an energy sliver at the mass of the black hole. A key result is that despite the manifest lack of smoothness, this single-sided pure state calculation yields precisely the Hartle-Hawking thermal correlator associated to the smooth horizon, in the small-$G_N$ limit. At finite $G_N$, there are variance corrections that are suppressed as $\mathcal{O}(e^{-S_{BH}/2})$. They become important at late times and resolve Maldacena's information paradox. Highly excited typical pure states on the stretched horizon vacuum are therefore models for black hole microstates, while the smooth horizon describes the thermal state. We note that heavy excited states on the stretched horizon are better defined than the vacuum itself. These results suggest that complementarity in the bulk EFT could arise from a UV complete bulk description in which the black hole interior is not manifest.

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arXiv2024

Moving Interfaces and two-dimensional Black Holes

Conformal field theories can exchange energy through a boundary interface. Imposing conformal boundary conditions for static interfaces implies energy conservation at the interface. Recently, the reflective and transmitive properties of such static conformal interfaces have been studied in two dimensions by scattering matter at the interface impurity. In this note, we generalize this to the case of dynamic interfaces. Motivated by the connections between the moving mirror and the black hole, we choose a particular profile for the dynamical interface. We show that a part of the total energy of each side will be lost in the interface. In other words, a time-dependent interface can accumulate or absorb energy. While, in general, the interface follows a time-like trajectory, one can take a particular limit of a profile parameter($β$), such that the interface approaches a null line asymptotically$(β\rightarrow 0)$. In this limit, we show that for a class of boundary conditions, the interface behaves like a `semipermeable membrane'. We also consider another set of conformal boundary conditions for which, in the null line limit, the interface mimics the properties expected of a horizon. In this case, we devise a scattering experiment, where (zero-point subtracted) energy from one CFT is fully transmitted to the other CFT, while from the other CFT, energy can neither be transmitted nor reflected, i.e., it gets lost in the interface. This boundary condition is also responsible for the thermal energy spectrum which mimics Hawking radiation. This is analogous to the black hole where the horizon plays the role of a one-sided `membrane', which accumulates all the interior degrees of freedom and radiates thermally in the presence of quantum fluctuation. Stimulated by this observation, we comment on some plausible construction of wormhole analogues.

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arXiv2023

Scrambling under quench

We evaluate out of time ordered correlators in certain low dimensional quantum systems at zero temperature, subjected to homogenous quantum quenches. We find that when the Lyapunov exponent exists, it can be identified with the quenched energy. We show that the exponent naturally gets related to the post-quench effective temperature. In the context of sudden quenches the exponent is determined in terms of the quench amplitude while for smooth quenches we observe scalings (both the Kibble-Zurek as well as the fast) of the exponent with the quench rate. The scalings are identical to that of the energy generated during the quench.

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arXiv2022

Brane Detectors of a Dynamical Phase Transition in a Driven CFT

We show that a dynamical transition from a non-heating to a heating phase of a periodic $SL(2,\mathbb{R})$ driven two-dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the non-heating phases. These metrics are different AdS$_{2}$ slices of the pure AdS$_{3}$ metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an end-of-world (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the non-heating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of two-point, four-point out-of-time correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.

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arXiv2022

Out-of-Time-Order correlators in driven conformal field theories

We compute Out-of-Time-Order correlators (OTOCs) for conformal field theories (CFTs) subjected to either continuous or discrete periodic drive protocols. This is achieved by an appropriate analytic continuation of the stroboscopic time. After detailing the general structure, we perform explicit calculations in large-$c$ CFTs where we find that OTOCs display an exponential, an oscillatory and a power-law behaviour in the heating phase, the non-heating phase and on the phase boundary, respectively. In contrast to this, for the Ising CFT representing an integrable model, OTOCs never display such exponential growth. This observation hints towards how OTOCs can demarcate between integrable and chaotic CFT models subjected to a periodic drive. We further explore properties of the light-cone which is characterized by the corresponding butterfly velocity as well as the Lyapunov exponent. Interestingly, as a consequence of the spatial inhomogeneity introduced by the drive, the butterfly velocity, in these systems, has an explicit dependence on the initial location of the operators. We chart out the dependence of the Lyapunov exponent and the butterfly velocities on the frequency and amplitude of the drive for both protocols and discuss the fixed point structure which differentiates such driven CFTs from their un-driven counterparts.

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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.

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arXiv2021

Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT$_2$

We construct an infinite class of eigenmodes with integer eigenvalues for the Vacuum Modular Hamiltonian of a single interval $N$ in 2d CFT and study some of its interesting properties, which includes its action on OPE blocks as well as its bulk duals. Our analysis suggests that these eigenmodes, like the OPE blocks have a natural description on the so called kinematic space of CFT$_2$ and in particular realize the Virasoro algebra of the theory on this kinematic space. Taken together, our results hints at the possibility of an effective description of the CFT$_2$ in the kinematic space language.

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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.

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arXiv2019

Spectrum of Modular Hamiltonian in the Vacuum and Excited States

We study the non-zero eigenmodes for the modular Hamiltonian in the context of AdS$_3/$CFT$_2$. We show how to perturbatively construct zero eigenmodes for the modular Hamiltonian of the class of excited states constructed in Lashkari et al.(arxiv:1811.05052), using information about the vacuum non-zero eigen modular modes.

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arXiv2019

Comments on spinning OPE blocks in AdS$_{3}$/CFT$_{2}$

We extend the work of \cite{Ferrara:1971vh},\cite{Ferrara:1973vz}, to obtain an integral expression of OPE blocks for spinning primaries in CFT$_{2}$. We observe, when the OPE blocks are made out of conserved spinning primaries, the integral becomes a product of two copies of weighted AdS$_{2}$ fields, smeared along geodesics. In this way, conserved current OPE blocks in CFT$_{2}$ have a different representation in terms of AdS$_{2}$ geodesic operators, in stead of viewing them as AdS$_{3}$ geodesic operators. We also show, how this representation can be related to AdS$_{3}$ massless higher spin fields through HKLL bulk field reconstruction. Using this picture, we consistently obtain the closed form expression of four point spinning conformal block as a product of two AdS$_{2}$ Geodesic Witten diagrams.

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arXiv2018

Modular Hamiltonians and large diffeomorphisms in $AdS_3$

We generalize the work of Kabat and Lifshytz (arXiv:1703.06523), of reconstructing bulk scalar fields using the intersecting modular hamiltonian approach discussed therein, to any locally $AdS_3$ space related to $AdS_3$ by large diffeomorphisms. We present several checks for our result including matcing with their result in appropriate limits as well as consistency with bulk diffeomorphisms. As a further check, from our expressions we also compute the first correction due to gravitational dressing to the bulk scalar field in $AdS_3$ and match with known results in the literature.

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arXiv2018

Entanglement entropy and kinematic space in BCFT and RG flow

The relation between kinematic space metric and entanglement entropy provides us with a differential equation for entanglement entropy. For BCFT on upper half plane we solve this equation to obtain an expression for entanglement entropy consistent with known results in the literature. We also discuss how this relation can be used to recast the RG flow, under relevant deformations of a CFT, as a flow in the space of kinematic space metrics.

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