arXiv subjects

Parijat Dey

Publications and source records attributed to Parijat Dey.

At least 19 recordsLinked to original sources

arXiv2026

Imprints of dynamical phases in semiclassical entanglement entropy in 2D CFT

We study the time evolution of semiclassical entanglement entropy in a class of $sl(2,\mathbb{R})$ driven states in a large $c$ conformal field theory (CFT) in $1+1$ spacetime dimensions. Upon varying the parameters of the drive, we find that the entanglement entropy exhibits the signature of the dynamical phases of the driven CFT. We further study the holographic dual of this CFT where the excited states of a minimally coupled scalar in $AdS_3$ induce a backreaction that modifies the background geometry. We compute the back reacted geometry by solving Einstein's equation with the expectation value of the stress tensor in the coherent state as the source term. Subsequently, we calculate the time evolution of the perturbed minimal area and the bulk entanglement entropy at $O(G_N^0)$, up to the sub-leading order in short distance approximation. These results match the CFT entanglement entropy in the boundary at $O(c^0)$, and serve as a nontrivial check of the Faulkner-Lewkowycz-Maldacena (FLM) conjecture for the first quantum correction of holographic entanglement entropy. The details of the check has been provided in the accompanying ancillary notebook.

hep-th↗

arXiv2026

Boundary conformal field theory, holography and bulk locality

We study bulk locality in a scalar effective field theory (EFT) in AdS background in presence of an end-of-the-world (EOW) brane. The holographic dual description is given in terms of a boundary conformal field theory (BCFT). We compute the two point correlation function of scalar operators in the BCFT using the one-loop Witten diagrams and compare its analytic structure with the constraints imposed by boundary conformal symmetry. We find that the loop-corrected correlator derived from a local bulk description is not fully compatible with BCFT expectations. This result places nontrivial constraint on bulk locality in holographic BCFT constructions and identifies BCFT correlators as sensitive probes of quantum bulk dynamics in presence of boundaries.

hep-th↗

arXiv2026

Geodesics, One Point Functions and Black Hole Perturbations

Holographic black holes exhibit a striking relation between thermal boundary one-point functions and bulk geodesic lengths. In the large conformal-dimension limit, the one-point function of a primary operator is given by the exponential of the geodesic length from its boundary insertion point to the horizon. We test the robustness of this relation under perturbations by considering a class of deformations of an Euclidean BTZ black hole and working to first order in the perturbation.We find that, at leading order in the large conformal-dimension limit and to first order in the radial horizon-preserving perturbation, the logarithmic variation of the one-point function is governed by the variation of the renormalized boundary-to-horizon geodesic length. The result is established using WKB and saddle-point methods, and WKB expressions at large conformal dimension are checked against the exact Green function and bulk-boundary propagator.

hep-th↗

arXiv2025

de Sitter locality from conformal field theory

An important insight from the study of AdS/CFT is that bulk locality can be derived from crossing symmetry of the boundary CFT. In this paper, we take the first steps in extending this statement to de Sitter background by demonstrating how to reconstruct a conformally coupled scalar effective field theory (EFT) with higher derivative interactions in four-dimensional de Sitter space from its in-in correlators. The latter can be computed from a certain EFT in Euclidean Anti-de Sitter space involving two scalar fields, which we derive from crossing symmetry of boundary correlators along with two novel constraints arising from unmixing anomalous dimensions of degenerate operators and equating them in different OPE channels. To facilitate the analysis, we work in Mellin space and apply dispersion relations to extract anomalous dimensions more efficiently.

hep-th↗

arXiv2024

Bootstrapping conformal defect operators on a line

We study a conformal field theory with cubic anisotropic symmetry in presence of a line defect. We compute the correlators of the low lying defect operators using Feynman diagrams and derive explicit expressions for the two, three and four point defect correlators at the cubic fixed point in $4-ε$ dimensions to $O(ε)$. We also compute the defect $g$-function for this setup and demonstrate that this is in agreement with the $g$-theorem, which states that the $g$-function is monotonic under the renormalisation group flow along the defect. Next, we focus on conformal bootstrap techniques to determine the CFT data associated with the defect operators, which is the main objective of the paper. We utilize the framework of crossing symmetric Polyakov bootstrap and compute the averaged CFT data to $O(ε)$ up to a finite number of ambiguities. We comment on unmixing the CFT data for the double trace operators at $O(ε)$ and use this to compute the $O(ε^2)$ data. Finally, we study these defect correlators non-perturbatively using numerical methods and isolate them near the free theory limit close to four dimensions.

hep-th↗

arXiv2024

Interacting conformal scalar in a wedge

We study a class of two-point functions in a conformal field theory near a wedge. This is a set-up with two boundaries intersecting at an angle $θ$. We compute it as a solution to the Dyson-Schwinger equation of motion for a quartic interaction in the $d=4-ε$ bulk and in the $d=3-ε$ boundary, up to order $\mathcal{O}(ε)$. We have extracted the anomalous dimensions from such correlators and we have complemented them with Feynman diagrams computations.

hep-th↗

arXiv2024

Bulk reconstruction in 2D multi-horizon black hole

The goal of the bulk reconstruction program is to construct boundary representations of fields in asymptotically Anti-de Sitter spacetimes. In this paper, we extend the program by computing the boundary representation of massless fields in an Achucarro-Ortiz black hole spacetime. We obtain analytic expressions for smearing functions in both the exterior and interior of the black hole. We also obtain expressions for Papadodimas-Raju mirror operators.

hep-th↗

arXiv2021

Bulk reconstruction and Bogoliubov transformations in AdS$_2$

In the bulk reconstruction program, one constructs boundary representations of bulk fields. We investigate the relation between the global/Poincare and AdS-Rindler representations for AdS$_2$. We obtain the AdS-Rindler smearing function for massive and massless fields and show that the global and AdS-Rindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdS-Rindler modes for both massive and massless particles.

hep-th↗

arXiv2021

Two applications of the analytic conformal bootstrap: A quick tour guide

We review the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are based solely on symmetries, in particular in the analytic structure and in the associativity of the operator product expansion. We focus on two applications of the analytic conformal bootstrap: the study of the $ε$ expansion of the Wilson Fisher model via the introduction of a dispersion relation and the large $N$ expansion of maximally supersymmetric Super Yang Mills theory in four dimensions.

hep-th↗

arXiv2021

On Analytic Bootstrap for Interface and Boundary CFT

We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation of motion to the boundary operator expansion. The method presented in this paper is general, and it is illustrated in the context of perturbative Wilson-Fisher theories. In particular, we find constraints on the OPE coefficients for the conformal interface CFT in $4 - ε$ dimensions (upto order $\mathcal{O}(ε^2)$) with $ϕ^4$-interactions in the bulk. We also compute the corresponding coefficients for the non-unitary $ϕ^3$-theory in $6 - ε$ dimensions in the presence of a conformal boundary equipped with either Dirichlet or Neumann boundary conditions upto order $\mathcal{O}(ε)$, or an interface upto order $\mathcal{O}(\sqrtε)$.

hep-th↗

arXiv2020

Operator expansions, layer susceptibility and two-point functions in BCFT

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function $\langleϕ_i ϕ^i\rangle$ of the O(N) model at the extraordinary transition in 4-$ε$ dimensional semi-infinite space to order $O(ε)$. The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order $O(ε^2)$. These agree with the known results both in $ε$ and large-N expansions.

hep-th↗

arXiv2019

Analytic Bootstrap for Logarithmic CFT

We study logarithmic conformal field theory (LogCFT) in four dimensions using conformal bootstrap techniques in the large spin limit. We focus on the constraints imposed by conformal symmetry on the four point function of certain logarithmic scalar operators and compute the leading correction to the anomalous dimension of double trace operators in the large spin limit. There exist certain holographic duals to such LogCFTs, which involve higher derivative equations of motion. The anomalous dimension is related to the binding energy of a state where two scalars rotate around each other with a large angular momentum. We compute this energy shift and compare it to the anomalous dimension of the large spin double trace operators due to stress tensor exchange in the LogCFT. Our result shows that the cluster decomposition principle is satisfied for LogCFTs as long as the dimensions of the operators are positive.

hep-th↗

arXiv2019

Dispersion Relation for CFT Four-Point Functions

We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity. Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously. In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators. As an application, the correlator $\langle ϕϕϕϕ\rangle$ in $ϕ^4$ theory at the Wilson-Fisher fixed point is computed in closed form to order $ε^2$ in the $ε$ expansion.

hep-th↗

arXiv2019

Mellin space bootstrap for global symmetry

We apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with $O(N)$ symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing symmetry in Mellin space. We solve the constraint equations to compute the anomalous dimension and the OPE coefficients of all operators quadratic in the fields in the epsilon expansion. We reproduce known results and derive new results up to $O(ε^3)$. For the $O(N)$ case, we also study the large $N$ limit in general dimensions and reproduce known results at the leading order in $1/N$.

hep-th↗

arXiv2018

Simplifying large spin bootstrap in Mellin space

We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials, we derive explicit expressions as an asymptotic expansion in inverse conformal spin to any order, reproducing the contribution of any primary operator and its descendants in the crossed channel. The expressions are in terms of known mathematical functions and involve generalized Bernoulli (Norlund) polynomials and the Mack polynomials and enable us to derive certain universal properties. Comparing with the recently introduced reformulated equations in terms of crossing symmetric tree level exchange Witten diagrams, we show that to leading order in anomalous dimension but to all orders in inverse conformal spin, the equations are the same as in the conventional formulation. At the next order, the polynomial ambiguity in the Witten diagram basis is needed for the equivalence and we derive the necessary constraints for the same.

hep-th↗

arXiv2017

Towards a Bootstrap approach to higher orders of epsilon expansion

We employ a hybrid approach in determining the anomalous dimension and OPE coefficient of higher spin operators in the Wilson-Fisher theory. First we do a large spin analysis for CFT data where we use results obtained from the usual and the Mellin Bootstrap and also from Feynman diagram literature. This gives new predictions at $O(ε^4)$ and $O(ε^5)$ for anomalous dimensions and OPE coefficients, and also provides a cross-check for the results from Mellin Bootstrap. These higher orders get contributions from all higher spin operators in the crossed channel. We also use the Bootstrap in Mellin space method for $ϕ^3$ in $d=6-ε$ CFT where we calculate general higher spin OPE data. We demonstrate a higher loop order calculation in this approach by summing over contributions from higher spin operators of the crossed channel in the same spirit as before.

hep-th↗

arXiv2016

More on analytic bootstrap for O(N) models

This note is an extension of a recent work on the analytical bootstrapping of $O(N)$ models. An additonal feature of the $O(N)$ model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor $(T_{μν})$ and the $ϕ_iϕ^i$ scalar, we also have other minimal twist operators as the spin-1 current $J_μ$ and the symmetric-traceless scalar in the case of $O(N)$. We determine the effect of these additional objects on the anomalous dimensions of the corresponding trace, symmetric-traceless and antisymmetric operators in the large spin sector of the $O(N)$ model, in the limit when the spin is much larger than the twist. As an observation, we also verified that the leading order results for the large spin sector from the $ε-$expansion are an exact match with our $n=0$ case. A plausible holographic setup for the special case when $N=2$ is also mentioned which mimics the calculation in the CFT.

hep-th↗

arXiv2014

Entanglement thermodynamics for an excited state of Lifshitz system

A class of (2+1)-dimensional quantum many body system characterized by an anisotropic scaling symmetry (Lifshitz symmetry) near their quantum critical point can be described by a (3+1)-dimensional dual gravity theory with negative cosmological constant along with a massive vector field, where the scaling symmetry is realized by the metric as an isometry. We calculate the entanglement entropy of an excited state of such a system holographically, i.e., from the asymptotic perturbation of the gravity dual using the prescription of Ryu and Takayanagi, when the subsystem is sufficiently small. With suitable identifications, we show that this entanglement entropy satisfies an energy conservation relation analogous to the first law of thermodynamics. The non-trivial massive vector field here plays a crucial role and contributes to an additional term in the energy relation.

hep-th↗