arXiv subjects

Vinayak Raj

Publications and source records attributed to Vinayak Raj.

16 recordsLinked to original sources

arXiv2026

Hironaka Geometry and Resurgence in Finite-$N$ Matrix Models

We study how finite-$N$ invariant theory organizes the non-perturbative structure of matrix models. For a model of four traceless Hermitian $2\times 2$ matrices, the Hironaka decomposition realizes the gauge-invariant configuration space as an eight-sheeted branched cover of the space of primary invariants. We show that ramification points of this cover naturally generate additional saddle points when the action depends only on the primaries. For an explicit rank-two saddle, we compute its action, one-loop normalization and Picard--Lefschetz connection to the perturbative vacuum. The same saddle controls the leading Borel singularity and large-order growth of perturbation theory, while its first fluctuation correction reproduces the first subleading large-order correction with no fitted parameters. Our results provide a concrete link between finite-$N$ invariant geometry and resurgence in matrix models.

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arXiv2025

$T\bar{T}$ braneworld holography

We study a constructive gravitational dual of two-dimensional $T\bar{T}$-deformed conformal field theories (CFTs) grounded in their two-dimensional gravity description. This framework can be viewed as a Randall-Sundrum-type braneworld, where two-dimensional gravity localized on the $AdS_3$ boundary is dynamical. Assuming the AdS/CFT correspondence, the holographic dictionary provides a straightforward translation between the $T\bar{T}$-deformed CFT and its gravitational dual. In particular, this $T\bar{T}$ braneworld holography remains valid in the presence of matter. To clarify how our framework relates to -- and differs from -- the cutoff AdS proposal, we examine, in the absence of matter, the effect of dynamical boundary gravity on the bulk geometry. In general, semiclassical integration of the boundary two-dimensional gravity -- weighted by the massive gravity action -- leads to a deformation of the two-dimensional metric on constant-radial surfaces. However, we find that the surface commonly interpreted as the cutoff emerges dynamically as a characteristic bulk surface on which the deformation is neutralized. This perspective opens the door to possible extensions of our framework to incorporate matter effects on the bulk surface in future work.

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arXiv2025

$T\bar{T}$-deformed correlators from a 2D gravity description

We study correlators in two-dimensional $T\bar{T}$-deformed conformal field theories by interpreting the $T\bar{T}$ deformation as a coupling to two-dimensional gravity. To demonstrate the utility of the massive gravity framework as a particular realization of the gravitational interpretation, we show how the $T\bar{T}$-deformed correlators at finite coupling can be computed by adopting a judicious parametrization of the 2D metric and a preferred choice of zweibeins. To illustrate how this method works in practice, we compute the leading logarithmic contributions to two- and three-point functions to all orders in the $T\bar{T}$ coupling, reproducing a known result while producing new findings. This framework generalizes the random geometry approach to finite coupling.

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arXiv2025

Nonperturbative effects in $T\bar{T}$-deformed conformal field theories: A toy model for Planckian physics

We propose a nonperturbative completion of two-point correlators in $T\bar{T}$-deformed conformal field theories (CFTs), and analyze their behavior at distance scales shorter than the fundamental length scale set by the $T\bar{T}$ deformation. Building on the interpretation of the $T\bar{T}$ deformation as a coupling to two-dimensional quantum gravity with a unique built-in length scale, we advance the study of $T\bar{T}$-deformed CFTs as a toy model for Planckian physics. As we probe shorter distances, trans-Planckian oscillations are followed by a super-Planckian regime in which correlations are typically suppressed by geometric randomness, in contrast to the power-law growth characteristic of CFTs. Moreover, their dependence on distance becomes exponentially weaker, suggesting that the underlying geometric structure has been largely erased -- a behavior broadly consistent with expectations for quantum spacetime in this regime.

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arXiv2025

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

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 Rényi reflected entropy through the partition function on replica manifold. The correction to the reflected entropy to the first order in the deformation parameter $μ$ 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

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 boundary conformal field theories and holographic moving mirrors

In this article, we investigate the entanglement structure of bipartite mixed states in (1+1)-dimensional boundary conformal field theories (BCFT$_2$s) through the odd entanglement entropy (OEE) by employing an appropriate replica technique. In this regard we compare our results with the bulk entanglement wedge cross section (EWCS) for AdS$_3$ geometries with an end-of-the-world brane. We observe consistent extension of the holographic duality between the difference of the OEE and the entanglement entropy (EE) with the bulk EWCS, in the framework of AdS$_3$/BCFT$_2$ holography. Furthermore, we also extend our computations to the holographic moving mirror models where the Hawking radiation from eternal and evaporating black holes may be simulated depending on certain mirror profiles, and find consistent extension of the aforementioned holographic duality.

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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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arXiv2022

Covariant holographic reflected entropy in $AdS_3/CFT_2$

We substantiate a covariant proposal for the holographic reflected entropy in $CFT$s dual to non-static $AdS$ geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the $AdS_3/CFT_2$ scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in $CFT_{1+1}$s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for these bulk geometries in the literature. This constitutes a significant consistency check for the proposal and its possible extension to the corresponding higher dimensional $AdS/CFT$ scenario.

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arXiv2022

Odd entanglement entropy in Galilean conformal field theories and flat holography

The odd entanglement entropy (OEE) for bipartite states in a class of $(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for $(2+1)$-dimensional asymptotically flat geometries dual to the $GCFT_{1+1}$ in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.

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arXiv2022

Reflected entropy in Galilean conformal field theories and flat holography

We obtain the reflected entropy for bipartite states in a class of $(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) through a replica technique. Furthermore we compare our results with the entanglement wedge cross section (EWCS) obtained for the dual (2+1) dimensional asymptotically flat geometries in the context of flat holography. We find that our results are consistent with the duality between the reflected entropy and the bulk EWCS for flat holographic scenarios.

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arXiv2022

Holographic Entanglement Negativity for Disjoint Subsystems in Conformal Field Theories with a Conserved Charge

We investigate the extension of a holographic construction for the entanglement negativity of two disjoint subsystems in proximity to $CFT_d$s with a conserved charge dual to bulk $AdS_{d+1}$ geometries. The construction involves a specific algebraic sum of the areas of bulk co-dimension two static minimal surfaces homologous to certain appropriate combinations of the subsystems in question. In this connection we compute the holographic entanglement negativity for two disjoint subsystems in proximity, with long rectangular strip geometries in $CFT_d$s dual to bulk non extremal and extremal RN-$AdS_{d+1}$ black holes. Our results conform to quantum information theory expectations and also reproduces earlier results for adjacent subsystems in the appropriate limit which constitutes strong consistency checks for our holographic construction.

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arXiv2022

Entanglement negativity, reflected entropy, and anomalous gravitation

We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS$_3$ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.

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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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arXiv2022

Entanglement Wedge in Flat Holography and Entanglement Negativity

We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual $(1+1)$-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual $AdS/CFT$ scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.

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