Thermodynamics of deformed AdS$_5$ model with a positive/negative quadratic correction in graviton-dilaton system

TL;DR

This paper develops a framework to solve black-hole backgrounds in deformed AdS$_5$ models with quadratic corrections, compares thermodynamic and loop operator results with lattice QCD, and finds a preference for positive quadratic correction.

Contribution

The paper introduces a self-consistent method to solve for black-hole backgrounds in deformed AdS$_5$ models with quadratic corrections and compares thermodynamic and loop operator results with lattice QCD data.

Findings

Bulk thermodynamics are insensitive to the sign of quadratic correction.

Results agree well with lattice QCD for pure SU(3) gauge theory.

Loop operators favor a positive quadratic correction.

Abstract

By solving the Einstein equations of the graviton coupling with a real scalar dilaton field, we establish a general framework to self-consistently solve the geometric background with black-hole for any given phenomenological holographic models. In this framwork, we solve the black-hole background, the corresponding dilaon field and the dilaton potential for the deformed AdS$_5$ model with a positive/negative quadratic correction. We systematically investigate the thermodynamical properties of the deformed AdS$_5$ model with a positive and negative quadratic correction, respectively, and compare with lattice QCD on the results of the equation of state, the heavy quark potential, the Polyakov loop and the spatial Wilson loop. We find that the bulk thermodynamical properties are not sensitive to the sign of the quadratic correction, and the results of both deformed holographic QCD models agree well with lattice QCD result for pure SU(3) gauge theory. However, the results from loop operators favor a positive quadratic correction, which agree well with lattice QCD result. Especially, the result from the Polyakov loop excludes the model with a negative quadratic correction in the warp factor of ${\rm AdS}_5$.