Holographic Correlators from Thermal Bootstrap

TL;DR

This paper introduces a novel method using the thermal bootstrap and Padé-Borel resummation to efficiently compute double-trace contributions in holographic thermal correlators, achieving rapid convergence and high accuracy.

Contribution

It develops a new approach combining the Euclidean periodicity condition with resummation techniques to accurately determine double-trace thermal coefficients.

Findings

Series converges rapidly with high numerical accuracy.

Method outperforms traditional PDE solving in efficiency.

Results agree well with existing PDE-based computations.

Abstract

Holographic thermal two-point functions can be analyzed using the operator product expansion which contains contributions from both multi-stress-tensor and double-trace operators. The former can be computed by analyzing the bulk equation of motion in a near-boundary expansion, but the latter has remained elusive-in practice, one resorts to solving a partial differential equation with limited accuracy. We show that imposing the Euclidean periodicity condition on the holographic correlator (also known as the KMS condition or thermal bootstrap), followed by Pad\'e-Borel resummation, provides an efficient method for computing double-trace thermal coefficients. The resulting series converges rapidly and yields numerical values in excellent agreement with those obtained from solving the partial differential equation.