Notes on Theta Dependence in Holographic Yang-Mills

TL;DR

This paper investigates how the theta parameter affects various physical observables in holographic 4d Yang-Mills theory, providing exact results and a comparison with lattice data to understand CP-breaking effects.

Contribution

It offers a comprehensive holographic analysis of theta dependence in Yang-Mills, including full backreaction and a simple rule for theta corrections to CP-neutral observables.

Findings

Qualitative agreement with lattice data on theta effects

Mass scale reduction by theta observed in holographic model

Exact theta results serve as benchmarks for Yang-Mills corrections

Abstract

Effects of the theta parameter are studied in Witten's model of holographic 4d Yang-Mills, where theta is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the theta parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the 't Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement - and thus the whole (T, theta) phase diagram - and the entanglement entropy. A simple rule is provided to derive the theta corrections to (at least) all the CP-neutral observables of the model. Some of the observables we consider can and have been in fact studied in pure 4d Yang-Mills on the lattice. In that framework the results, obtained in the small theta regime, are given up to very few powers of theta^2. The corresponding holographic results agree qualitatively with available lattice data and signal an overall mass scale reduction by theta. Moreover, being exact in theta, they provide a benchmark for higher order corrections in Yang-Mills.