arXiv subjects

Debarshi Basu

Publications and source records attributed to Debarshi Basu.

At least 19 recordsLinked to original sources

arXiv2026

PEE threads and bit-threads in BTZ black brane and finite-cutoff AdS$_3$

We develop PEE thread flows for the planar BTZ black brane and finite-cutoff holography. Exact geodesic-distance kernels define source-resolved PEE thread currents whose superposition gives divergenceless bit-thread fields. In BTZ, boundary-boundary and boundary-horizon sectors reproduce the entanglement contour and thermal horizon flux. At finite cutoff, the two-point PEE kernels are smooth and select macroscopic flows that are generically non-geodesic despite being built from geodesic elementary threads. We compare these PEE-selected flows with independent normal-geodesic bit-thread flows and show that they saturate the same RT bottleneck while differing in boundary calibration, endpoint pairing and off-bottleneck structure. The resulting constructions make explicit both the endpoint organization of finite-cutoff entanglement and the nonuniqueness of holographic max flows.

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arXiv2026

PEE threads and bit threads in gravitational subregions of AdS

Motivated by the kinematic-space description of gravitational subregions \cite{Basu:2026hbg}, we allow partial entanglement entropy (PEE) threads to be sourced not only from the asymptotic boundary, but also from boundaries of subregions. Based on this setup, we develop a framework to construct configurations for PEE threads and bit threads sourced from surfaces in the AdS bulk. The situations we have analyzed include the Poincar\'e AdS$_3$ and the planar BTZ black brane with an end-of-the-world (EOW) brane, and the entanglement wedges of boundary multi-intervals. We construct novel configurations of PEE threads and bit threads in these situations, which shed new light in our understanding of the AdS$_3$/BCFT$_2$ correspondence and the holography defined in the entanglement wedge motivated by surface/state correspondence. A notable feature we found is that, although the elementary PEE threads are geodesics, the integral curves of the coarse-grained bit-thread current are generically not geodesics. Across the explicit constructions, the integrated source currents reduce to endpoint distance-difference potentials, which make divergencelessness, the norm bound and bottleneck saturation geometrically transparent. Our results clarify how boundary, brane, horizon and RT-surface degrees of freedom participate in holographic entanglement and provide a concrete link between PEE, bit threads, subregion kinematic space and the surface/state correspondence.

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arXiv2026

Holography and Kinematic Space for Gravitational Sub-regions in AdS

It is well-known in integral geometry that a maximally symmetric Riemannian manifold, such as a static slice of vacuum AdS spacetime, can be perfectly covered by the geodesics in the Kinematic space, which we call the partial-entanglement-entropy (PEE) threads. In this context, the area of a codimension-one surface in the manifold can be computed by counting its intersections with the PEE threads, which is the celebrated Crofton formula. In this paper, we analyze the Kinematic space for a generic subregion in vacuum AdS space, and propose that the PEE threads emanate from a co-dimension one surface can perfectly cover a subregion in the manifold. Furthermore, we build holographic tensor network models on the network of the PEE threads confined in a subregion, thereby providing a concrete framework that realizes the surface-state correspondence and the generalized entanglement wedges for gravitational subregions.

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arXiv2026

Butterflies in $\textrm{T}\overline{\textrm{T}}$ deformed anomalous CFT$_2$

We study quantum chaos in $\textrm{T}\overline{\textrm{T}}$-deformed two-dimensional conformal field theories with gravitational anomaly and their holographic dual description in topologically massive gravity. Using pole-skipping and shock-wave analysis, we extract the Lyapunov exponent and butterfly velocity and analyze the interplay between irrelevant deformation and parity-violating dynamics. We find that the chaos bound remains saturated, while the butterfly velocity exhibits nontrivial dependence on the deformation parameter and anomaly. We also identify a Hagedorn regime in which the chaotic response becomes complex valued, signaling a breakdown of the physical branch of the deformed theory.

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arXiv2025

The holographic $\textrm{T}\overline{\textrm{T}}$ deformation of the CFT$_2$ with gravitational anomalies

We develop the holographic framework for the $\textrm{T}\overline{\textrm{T}}$ deformation of two-dimensional conformal field theories (CFT$_2$) with gravitational anomalies, characterized by unequal left and right central charges and holographically dual to topological massive gravity (TMG). Utilizing the mixed boundary condition prescription, we construct the deformed BTZ black hole geometry and derive the corresponding deformed energy spectrum, confirming that the universal flow equation remains valid despite the presence of gravitational anomalies. From the boundary perspective, we compute leading-order corrections to entanglement entropy and reflected entropy induced by the $\textrm{T}\overline{\textrm{T}}$ deformation, as well as the balanced partial entanglement entropy non-perturbatively. On the gravity side, these quantities are evaluated using spinning worldlines in the deformed bulk geometry, with results matching their field-theoretic counterparts in the high-temperature limit. We further analyze the reality condition for holographic entanglement entropy, which constrains the deformation parameter and reveals a generalized Hagedorn behavior. This Hagedorn-like transition is also independently reproduced from the asymptotic density of states in the deformed anomalous CFT$_2$, providing additional evidence for its universality.

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arXiv2025

Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation

These notes present a comprehensive analysis of shockwave geometries in holographic settings, focusing on $\textrm{T}\overline{\textrm{T}}$-deformed BTZ black holes and their extensions. By constructing deformed metrics and employing Kruskal coordinates, we examine out-of-time-ordered correlators (OTOCs) as probes of quantum chaos. We also study localized shockwave solutions and analyze their backreaction, highlighting regimes in which the Mezei-Stanford bound on the butterfly velocity is potentially violated. The results obtained via shockwave methods are corroborated with recent developments in pole-skipping phenomena and the entanglement wedge approach, demonstrating consistency among distinct probes of chaos in holographic theories.

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arXiv2025

Reflected entropy and islands in a braneworld cosmology

This work investigates the nature of mixed state entanglement and correlation in a braneworld cosmological model, where the bulk geometry is described by an eternal BTZ black hole truncated by an end-of-the-world brane representing a Friedmann-Robertson-Walker (FRW) cosmology. We explore the holographic reflected entropy for both adjacent and disjoint subsystems using the island prescription and the defect extremal surface prescription. In the large central charge limit, we demonstrate that both prescriptions yield an exact agreement. Additionally, we analyze the time evolution of reflected entropy and holographic mutual information, along with an analysis of the geometric Markov gap. Our study provides new insights into the role of quantum extremal surfaces in probing black hole interiors and cosmological spacetimes, with implications for understanding mixed state entanglement and quantum information dynamics in holographic cosmological models.

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arXiv2024

Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy

We investigate the reflected entropy for bipartite mixed state configurations in a $T\bar{T}$ deformed boundary conformal field theory in $2$ dimensions (BCFT$_2$). The bulk dual is described by asymptotically AdS$_3$ geometries with the cut off surface pushed deeper into the bulk and truncated by an end of the world brane. We obtain the reflected entropy up to a linear order in the radial cut-off for static and time dependent configurations involving an eternal black hole, from the island and defect extremal surface (DES) prescriptions in the context of the deformed AdS/BCFT. We observe agreement of the leading order correction for all cases between the two prescriptions. We also obtain the analogous of the Page curves for the reflected entropy and investigate the modification due to the $T\bar{T}$ deformation.

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arXiv2024

Entanglement, $\textrm{T}\bar{\textrm{T}}$ and rotating black holes

In this work, we investigate the entanglement structure in a $\textrm{T}\bar{\textrm{T}}$-deformed holographic CFT$_2$ with a conserved angular momentum. We utilize conformal perturbation theory to compute the leading order correction to the entanglement entropy and the reflected entropy due to the $\textrm{T}\bar{\textrm{T}}$ deformation in the limit of large central charge. In the dual bulk perspective described by a rotating BTZ black hole with a finite radial cut-off, we compute the holographic entanglement entropy and the entanglement wedge cross-section and observe perfect agreement with our field theoretic computation for small values of the deformation parameter.

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arXiv2024

Reflected entropy and timelike entanglement in $\textrm{T}\bar{\textrm{T}}$ deformed CFT$_2$s

We develop a covariant formalism to investigate the mixed state entanglement structure of time-dependent boosted subsystems in $\textrm{T}\bar{\textrm{T}}$ deformed CFT$_2$s through the reflected entropy. To this end we utilize the conformal perturbation theory to obtain the R\'enyi reflected entropy through the partition function on replica manifold. The correction to the reflected entropy to the first order in the deformation parameter $\mu$ in then obtained in the replica limit for finite temperature and finite sized systems. We verify our field theoretic computations by obtaining the dual EWCS in the corresponding bulk cut-off AdS$_3$ geometries and find perfect agreement between the two.

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arXiv2023

Holographic Reflected Entropy and Islands in Interface CFTs

We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS$_3$/ICFT$_2$ framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT$_{\text{2}}$ which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS$_3$ geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS$_2$ interface brane, which is dual to an ICFT$_2$ in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT$_{\text{2}}$s coupled to an AdS$_2$ brane. We demonstrate that the results from the island formula match precisely with the bulk AdS$_3$ results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS$_2$ black hole.

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arXiv2023

Reflected entropy in BCFTs on a black hole background

We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in two dimensional boundary conformal field theories (BCFT$_2$s) in a black hole background. The bulk dual is described by an AdS$_3$ black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT$_2$ verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.

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arXiv2023

Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT$_2$s and holography

We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in $\text{T}\bar{\text{T}}$ deformed CFT$_2$s. This framework is then utilized to obtain the leading order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in $\text{T}\bar{\text{T}}$ deformed thermal CFT$_2$s in the large central charge limit. The field theory results are subsequently reproduced in the high temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cut-off BTZ geometries. We further show that for finite size $\text{T}\bar{\text{T}}$ deformed CFT$_2$s at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.

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arXiv2023

Islands and dynamics at the interface

We investigate a family of models described by two holographic CFT$_2$s coupled along a shared interface. The bulk dual geometry consists of two AdS$_3$ spacetimes truncated by a shared Karch-Randall end-of-the-world (EOW) brane. A lower dimensional effective model comprising of JT gravity coupled to two flat CFT$_2$ baths is subsequently realized by considering small fluctuations on the EOW brane and implementing a partial Randall-Sundrum reduction where the transverse fluctuations of the EOW brane are identified as the dilaton field. We compute the generalized entanglement entropy for bipartite states through the island prescription in the effective lower dimensional picture and obtain precise agreement in the limit of large brane tension with the corresponding doubly holographic computations in the bulk geometry. Furthermore, we obtain the corresponding Page curves for the Hawking radiation in this JT braneworld.

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arXiv2023

Ownerless island and partial entanglement entropy in island phases

In the context of partial entanglement entropy (PEE), we study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. The self-encoding property of the island phase changes the way we evaluate the PEE. With the contributions from islands taken into account, we give a generalized prescription to construct PEE and balanced partial entanglement entropy (BPE). Here the ownerless island region, which lies inside the island $\text{Is}(AB)$ of $A\cup B$ but outside $\text{Is}(A)\cup \text{Is}(B)$, plays a crucial role. Remarkably, we find that under different assignments for the ownerless island, we get different BPEs, which exactly correspond to different saddles of the entanglement wedge cross-section (EWCS) in the entanglement wedge of $A\cup B$. The assignments can be settled by choosing the one that minimizes the BPE. Furthermore, under this assignment we study the PEE and give a geometric picture for the PEE in holography, which is consistent with the geometric picture in the no-island phases.

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arXiv2023

Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT$_2$s

We apply a suitable replica technique to develop a perturbative expression for the entanglement negativity of bipartite mixed states in T$\overline{\text{T}}$-deformed CFT$_2$s up to the first order in the deformation parameter. Utilizing our perturbative construction we compute the entanglement negativity for various bipartite mixed states involving two disjoint intervals, two adjacent intervals, and a single interval in a T$\overline{\text{T}}$-deformed CFT$_2$ at a finite temperature, in the large central charge limit. Subsequently, we advance appropriate holographic constructions to compute the entanglement negativity for such bipartite states in T$\overline{\text{T}}$-deformed thermal CFT$_2$s dual to BTZ black holes in a finite cut-off bulk geometry and find agreement with the corresponding field theoretic results in the limit of small deformation parameter.

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arXiv2022

Entanglement Islands from Hilbert Space Reduction

In this paper we propose a mechanism to generate entanglement islands in quantum systems from a purely quantum information perspective. More explicitly we show that, if we impose certain constraints on a quantum system by projecting out certain states in the Hilbert space, it is possible that for all the states remaining in the reduced Hilbert space, there exits subsets $I_a$ whose states are encoded in the states of another subset $\mathcal{R}_a$. Then the subsets $\{I_a\}$ are just the entanglement islands of the corresponding subsets $\{\mathcal{R}_a\}$. We call such a system self-encoded, and find that the entanglement entropy in such systems should be calculated by a new island formula. We give a comparison between our new island formula and island formula in gravitational theories. Inspired by our mechanism, we propose a simulation of the AdS/BCFT correspondence and the island phases in this context via a holographic CFT$_2$ with a special Weyl transformation.

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arXiv2022

Defect extremal surfaces for entanglement negativity

We propose a doubly holographic version of the semi-classical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the AdS bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semi-classical island formula for the entanglement negativity is demonstrated in AdS$_3$/BCFT$_2$ framework. Furthermore, in the time-dependent AdS$_3$/BCFT$_2$ scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulae and obtain the analogues of the Page curves.

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