Holographic theories at finite $\theta$-angle, CP-violation, glueball spectra and strong-coupling instabilities

TL;DR

This paper explores holographic theories with a nonzero theta-angle, analyzing their ground states, glueball spectra, and CP-violation effects, revealing how glueball masses decrease with increasing theta and indicating potential instabilities.

Contribution

It provides a comprehensive analysis of holographic models with a theta-angle, including ground-state solutions, glueball spectra, and CP-violation, highlighting the effects of different potentials and instabilities.

Findings

Glueball masses decrease monotonically with theta-angle.

Steep dilaton potentials lead to negative glueball mass squared, indicating instabilities.

Instanton condensation is favored in certain bulk conditions.

Abstract

A general class of holographic theories with a nontrivial $\theta$-angle are analyzed. The instanton density operator is dual to a bulk axion field. We calculate the ground-state solutions with nontrivial source, $a_{UV}$, for the axion, for both steep and soft dilaton potentials in the IR, and both in $d=3$ and $d=4$. We find all cases to be qualitatively similar. We also calculate the spin$=2,0$ glueball spectra and show that the glueball masses monotonically decrease as functions of $a_{UV}$ (or $\theta$-angle). The slopes of glueball masses are different, generically, in different potentials. In the case of steep dilaton potentials, the glueball (masses)$^2$ turn negative before the maximum of $a_{UV}$ is attained. We interpret this as a signal for a favored instanton condensation in the bulk. We also investigate strong CP-violation in the effective glueball action.