The theta-dependent Yang-Mills theory at finite temperature in a holographic description

TL;DR

This paper uses holographic duality to analyze a theta-dependent Yang-Mills theory at finite temperature, revealing asymptotic freedom, suppressed theta effects at high temperature, and a geometric interpretation of theta dependence.

Contribution

It provides an analytical supergravity solution for a D0-D4 brane system modeling theta-dependent Yang-Mills theory at finite temperature, with new insights into its thermodynamic and topological properties.

Findings

Coupling constant shows asymptotic freedom behavior.

Theta dependence on free energy is suppressed at high temperature.

Topological susceptibility vanishes in the large N_c limit.

Abstract

The theta-dependent gauge theories can be studied by using holographic duality through string theory on certain spacetimes. Via this correspondence we consider a stack of $N_{0}$ dynamical D0-branes as D-instantons in the background sourced by $N_{c}$ coincident non-extreme black D4-branes. According to the gauge-gravity duality this D0-D4 brane system corresponds to Yang-Mills theory with a theta angle at finite temperature. We solve the IIA supergravity action by taking account into a sufficiently small backreaction of the D-instantons and obtain an analytical solution for our D0-D4-brane configuration. Then the dual theory in the large $N_{c}$ limit can be holographically investigated with the gravity solution. In the dual field theory, we find the coupling constant exhibits the property of asymptotic freedom as it is expected in QCD. The contribution of the theta-dependence to the free energy gets suppressed at high temperature which is basically consistent with the calculation by using the Yang-Mills instanton. The topological susceptibility in the large $N_{c}$ limit vanishes and this behavior remarkably agrees with the implications from the simulation results at finite temperature. Besides we finally find a geometrical interpretation of the theta-dependence in this holographic system.