arXiv subjects

Rahul Poddar

Publications and source records attributed to Rahul Poddar.

9 recordsLinked to original sources

arXiv2024

R\'enyi entropy of single-character CFTs on the torus

We introduce a nonperturbative approach to calculate the R\'enyi entropy of a single interval on the torus for single-character (meromorphic) conformal field theories. Our prescription uses the Wro\'nskian method of Mathur, Mukhi, and Sen [Nucl. Phys. B312, 15 (1989)], in which we construct differential equations for torus conformal blocks of the twist two-point function. As an illustrative example, we provide a detailed calculation of the second R\'enyi entropy for the $\rm E_{8,1}$ Wess-Zumino-Witten (WZW) model. We find that the $\mathbb Z_2$ cyclic orbifold of a meromorphic conformal field theory (CFT) results in a four-character CFT which realizes the toric code modular tensor category. The $\mathbb Z_2$ cyclic orbifold of the $\rm E_{8,1}$ WZW model, however, yields a three-character CFT since two of the characters coincide. We then compute the torus conformal blocks and find that the twist two-point function, and therefore the R\'enyi entropy, is two-periodic along each cycle of the torus. The second R\'enyi entropy for a single interval of the $\rm E_{8,1}$ WZW model has the universal logarithmic divergent behavior in the decompactification limit of the torus, as expected as well as the interval approaches the size of the cycle of the torus. Furthermore, we see that the $q$-expansion is UV finite, apart from the leading universal logarithmic divergence. We also find that there is a divergence as the size of the entangling interval approaches the cycle of the torus, suggesting that gluing two tori along an interval the size of a cycle is a singular limit.

hep-th↗

arXiv2024

On The Triviality Of $m$-Modified Conformal Vector Fields

We prove that a compact Riemannian manifold $M$ does not admit any non-trivial $m$-modified homothetic vector fields. In the corresponding case of an $m$-modified conformal vector field $V$, we establish an inequality that implies the triviality of $V$. Further, we demonstrate that an affine Killing $m$-modified conformal vector field on a non-compact Riemannian manifold $M$ must be trivial. Finally, we show that an $m$-modified gradient conformal vector field is trivial under the assumptions of polynomial volume growth and convergence to zero at infinity.

math.DG↗

arXiv2024

Extended Solitons of the Ambient Obstruction Flow

In this paper we expand on the work of the first author on ambient obstruction solitons, which are self-similar solutions to the ambient obstruction flow. Our main result is to show that any closed ambient obstruction soliton is ambient obstruction flat and has constant scalar curvature. We show, in fact, that the first part of this result is true for a more general extended soliton equation where we allow an arbitrary conformal factor to be added to the equation. We discuss how this implies that, on a compact manifold, the ambient obstruction flow has no fixed points up to conformal diffeomorphism other than ambient obstruction flat metrics. These results are the consequence of a general integral inequality that can be applied to the solitons to any geometric flow. Additionally, we use these results to obtain a generalization of the Bourguignon-Ezin identity on a closed Riemannian manifold and study the converse problem on a closed extended $q$-soliton. We also study this extended equation further in the case of homogeneous and product metrics.

math.DG↗

arXiv2023

A generalized Selberg zeta function for flat space cosmologies

Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds $\mathcal M/\mathbb Z$, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results.

hep-th↗

arXiv2023

$T \overline T$-Deformations of Holographic Warped CFTs

We explore $T \overline T$ deformations of Warped Conformal Field Theories (WCFTs) in two dimensions as examples of $T\overline T$ deformed non-relativistic quantum field theories. WCFTs are quantum field theories with a Virasoro$\times$U(1) Kac-Moody symmetry. We compute the deformed symmetry algebra of a $T\overline T$ deformed holographic WCFT, using the asymptotic symmetries of AdS$_3$ with $T \overline T$ deformed Comp\'ere, Song and Strominger (CSS) boundary conditions. The U(1) Kac-Moody symmetry survives provided one allows the boundary metric to transform under the asymptotic symmetry. The Virasoro sector remains but is now deformed and no longer chiral.

hep-th↗

arXiv2022

A Selberg zeta function for warped AdS$_3$ black holes

The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS$_3$ black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS$_3$ black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds.

hep-th↗

arXiv2020

Universal Correlators and Novel Cosets in 2d RCFT

The two-character level-1 WZW models corresponding to Lie algebras in the Cvitanovi\'c-Deligne series $A_1,A_2,G_2,D_4,F_4,E_6,E_7$ have been argued to form coset pairs with respect to the meromorphic $E_{8,1}$ CFT. Evidence for this has taken the form of holomorphic bilinear relations between the characters. We propose that suitable 4-point functions of primaries in these models also obey bilinear relations that combine them into current correlators for $E_{8,1}$, and provide strong evidence that these relations hold in each case. Different cases work out due to special identities involving tensor invariants of the algebra or hypergeometric functions. In particular these results verify previous calculations of correlators for exceptional WZW models, which have rather subtle features. We also find evidence that the intermediate vertex operator algebras A$_{0.5}$ and E$_{7.5}$, as well as the three-character A$_{4,1}$ theory, also appear to satisfy the novel coset relation.

hep-th↗

arXiv2020

Rational CFT With Three Characters: The Quasi-Character Approach

Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two characters. These in turn generate all possible admissible characters, of arbitrary Wronskian index, in order two. Here we initiate a study of the three-character case. We conjecture several infinite families of quasi-characters and show in examples that their linear combinations an generate admissible characters with arbitrarily large Wronskian index. The structure is completely different from the order two case, and the novel coset construction of arXiv:1602.01022 plays a key role in discovering the appropriate families. Using even unimodular lattices, we construct some explicit three-character CFT corresponding to the new admissible characters.

hep-th↗

arXiv2019

Contour Integrals and the Modular S-Matrix

We investigate a conjecture to describe the characters of large families of RCFT's in terms of contour integrals of Feigin-Fuchs type. We provide a simple algorithm to determine the modular S-matrix for arbitrary numbers of characters as a sum over paths. Thereafter we focus on the case of 2, 3 and 4 characters, where agreement between the critical exponents of the integrals and the characters implies that the conjecture is true. In these cases, we compute the modular S-matrix explicitly, verify that it agrees with expectations for known theories, and use it to compute degeneracies and multiplicities of primaries. We also compute S in an 8-character example to provide additional evidence for the original conjecture. On the way we note that the Verlinde formula provides interesting constraints on the critical exponents of RCFT in this context.

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