arXiv subjects

Semanti Dutta

Publications and source records attributed to Semanti Dutta.

8 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

$SO(1, d + 1)$ symmetry of the Exact RG equation

There is a method for constructing from first principles, a holographic bulk dual action in Euclidean $AdS_{d+1}$ space for a $d$-dimensional Euclidean CFT on the boundary, starting from the Polchinski's Exact Renormalization Group (ERG) equation that describes the RG evolution of the interaction part of the boundary Wilson action. The bulk action in $AdS_{d+1}$ has an $SO(1,d+1)$ symmetry and is obtained from the evolution operator of the Polchinski's ERG equation by a map that involves a field redefinition and requires a $\textit{special}$ form of the UV cutoff function in the ERG equation. In this paper, we show that for $\textit{any form}$ of the cutoff function, the ERG evolution operator has an $SO(1,d+1)$ symmetry. The generators of the special conformal transformation depend on the cutoff function. For the special cutoff function that maps to $AdS$ space, the transformations have the standard form of $AdS$ isometry. We also show that the ERG evolution operator for the $\textit{full}$ Wilson action can be put in the same form as the Polchinski's ERG equation by a field redefinition and consequently also has an $SO(1,d+1)$ symmetry for any cutoff function.

hep-th↗

arXiv2025

Precision tests of bulk entanglement: $AdS_3$ vectors

We consider single-particle excitations of the massive Chern-Simons field of mass $M$ in $AdS_3$ and evaluate their contribution at the first sub-leading order in $G_N$ to the entanglement entropy across the Ryu-Takayanagi surface. Quantizing the Chern-Simons field in $AdS_3$, we evaluate the corrections to the holographic entanglement entropy using the Faulkner-Lewkowycz-Maldacena formula. The massive Chern-Simons field also obeys the equations of motion of a massive vector in $AdS_3$. The lowest-energy single-particle excitation of this field is dual to the primary operator of conformal dimension $M+1$ with spin one in the dual CFT; all other single-particle excitations are dual to its global descendants. We compare the entanglement entropy result from the FLM formula to the single-interval entanglement entropy in large-charge holographic CFT obtained using the replica trick for the primary and its tower of holomorphic descendants. The two results agree precisely in the leading and sub-leading terms of the short interval expansion. We evaluate the contribution of the edge mode to the vacuum-subtracted entanglement and show that it vanishes, which is crucial for the FLM formula to agree with the CFT result. On taking the massless limit, the result coincides with the contribution of a $U(1)$ current to the single interval entanglement entropy. This is surprising since an earlier calculation in the literature reproduced the CFT result entirely from the edge $U(1)$ degrees of freedom on the RT surface.

hep-th↗

arXiv2024

Precision tests of bulk entanglement entropy

We consider linear superpositions of single particle excitations in a scalar field theory on $AdS_3$ and evaluate their contribution to the bulk entanglement entropy across the Ryu-Takayanagi surface. We compare the entanglement entropy of these excitations obtained using the Faulkner-Lewkowycz-Maldacena formula to the entanglement entropy of linear superposition of global descendants of a conformal primary in a large $c$ CFT obtained using the replica trick. We show that the closed from expressions for the entanglement entropy in the small interval expansion both in gravity and the CFT precisely agree. The agreement serves as a non-trivial check of the FLM formula for the quantum corrections to holographic entropy which also involves a contribution from the back reacted minimal area. Our checks includes an example in which the state is time dependent and spatially in-homogenous as well another example involving a coherent state with a Bañados geometry as its holographic dual.

hep-th↗

arXiv2023

Bulk Gauge Fields and Holographic RG from Exact RG

Recently, a method was described for deriving Holographic RG equation in $AdS_{D+1}$ space starting from an Exact RG equation of a $D$-dimensional boundary CFT (Sathiapalan, Sonoda, 2017). The evolution operator corresponding to the Exact RG equation was rewritten as a functional integral of a $D+1$ dimensional field theory in $AdS_{D+1}$ space. This method has since been applied to elementary scalars and composite scalars in the $O(N)$ model (Sathiapalan, 2020). In this paper, we apply this technique to the conserved vector current and the energy momentum tensor of a boundary CFT, the $O(N)$ model at a fixed point. These composite spin one and spin two operators are represented by auxiliary fields and extend into the bulk as gauge fields and metric perturbations. We obtain, at the free level, the (gauge fixed) Maxwell and Einstein actions. While the steps involved are motivated by the AdS/CFT correspondence, none of the steps logically require the AdS/CFT conjecture for their justification.

hep-th↗

arXiv2023

Aspects of the map from Exact RG to Holographic RG in AdS and dS

In earlier work the evolution operator for the exact RG equation was mapped to a field theory in Euclidean AdS. This gives a simple way of understanding AdS/CFT. We explore aspects of this map by studying a simple example of a Schroedinger equation for a free particle with time dependent mass. This is an analytic continuation of an ERG like equation. We show for instance that it can be mapped to a harmonic oscillator. We show that the same techniques can lead to an understanding of dS/CFT too.

hep-th↗

arXiv2022

Wilson Action for the $O(N)$ Model

In this paper the fixed-point Wilson action for the critical $O(N)$ model in $D=4-\eps$ dimensions is written down in the $\eps$ expansion to order $\eps^2$. It is obtained by solving the fixed-point Polchinski Exact Renormalization Group equation (with anomalous dimension) in powers of $\eps$. This is an example of a theory that has scale and conformal invariance despite having a finite UV cutoff. The energy-momentum tensor for this theory is also constructed (at zero momentum) to order $\eps^2$. This is done by solving the Ward-Takahashi identity for the fixed point action. It is verified that the trace of the energy-momentum tensor is proportional to the violation of scale invariance as given by the exact RG, i.e., the $β$ function. The vanishing of the trace at the fixed point ensures conformal invariance. Some examples of calculations of correlation functions are also given.

hep-th↗

arXiv2022

Finite Cutoff CFT's and Composite Operators

Recently a conformally invariant action describing the Wilson-Fischer fixed point in $D=4-ε$ dimensions in the presence of a {\em finite} UV cutoff was constructed \cite{Dutta}. In the present paper we construct two composite operator perturbations of this action with definite scaling dimension also in the presence of a finite cutoff. Thus the operator (as well as the fixed point action) is well defined at all momenta $0\leq p\leq \infty$ and at low energies they reduce to $\int_x ϕ^2$ and $\int _x ϕ^4$ respectively. The construction includes terms up to $O(\lamda^2)$. In the presence of a finite cutoff they mix with higher order irrelevant operators. The dimensions are also calculated to this order and agree with known results.

hep-th↗