Holographic U(1)_A and String Creation

TL;DR

This paper investigates the U(1)_A problem in holographic QCD, showing how axial symmetry breaking varies across phases and linking it to string and instanton effects in the Sakai-Sugimoto model.

Contribution

It demonstrates the phase-dependent behavior of axial symmetry breaking and introduces a holographic description involving spacelike strings and D0-branes.

Findings

Axial symmetry is broken at order 1/N_c in the confining phase.

In the deconfined phase, the symmetry remains unbroken to all orders in 1/N_c.

The symmetry breaking condensate is represented by spacelike strings between D0-branes and D8-branes.

Abstract

We analyze the resolution of the U(1)_A problem in the Sakai-Sugimoto holographic dual of large N_c QCD at finite temperature. It has been shown that in the confining phase the axial symmetry is broken at order 1/N_c, in agreement with the ideas of Witten and Veneziano. We show that in the deconfined phase the axial symmetry remains unbroken to all orders in 1/N_c. In this case the breaking is due to instantons which are described by spacelike D0-branes, in agreement with 'tHooft's resolution. The holographic dual of the symmetry breaking fermion condensate is a state of spacelike strings between the D0-brane and the flavor D8-branes, which result from a spacelike version of the string creation effect. In the intermediate phase of deconfinement with broken chiral symmetry the instanton gas approximation is possibly regulated in the IR, which would imply an eta' mass-squared of order exp(-N_c).