arXiv subjects

Danilo E. Díaz

Publications and source records attributed to Danilo E. Díaz.

3 recordsLinked to original sources

arXiv2025

On heat coefficients, multiplicative anomaly and 4D Casimir energy for GJMS operators

This note aims to verify a prediction on the total derivative term of the 4D trace anomaly, and the corresponding heat coefficient, for GJMS operators. It stems from the explicit computation of an {\it improved} Casimir (or vacuum) energy on the sphere that takes into account the multiplicative anomaly among the (shifted) Laplacian factors and connects, via the Cappelli-Coste relation, with both the type A central charge and the total derivative term of the 4D trace anomaly. The present heat coefficient computation is based on Juhl's explicit formula for GJMS operators, Gilkey's formula for the integrated heat coefficient of higher-order Laplacians, and the \textit{conformal principle} by Branson and Ørsted.

hep-th↗

arXiv2009

Holographic formula for the determinant of the scattering operator in thermal AdS

A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence of a quantum correction to the partition function in the bulk and the corresponding subleading correction at large N on the boundary. In this paper we probe this prediction for a class of quotients of hyperbolic space by a discrete subgroup of isometries. We restrict to the simplest situation of an abelian group where the quotient geometry describes thermal AdS and also the non-spinning BTZ instanton. The bulk computation is explicitly done using the method of images and the answer can be encoded in a (Patterson-)Selberg zeta-function.

hep-th↗

arXiv2008

Partition functions and double-trace deformations in AdS/CFT

We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each other: bulk and boundary computations, as well as their formal identity. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuational determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.

hep-th↗