Boundary terms in the Witten-Sakai-Sugimoto model at finite density

TL;DR

This paper investigates boundary terms in the Witten-Sakai-Sugimoto holographic model at finite density, addressing discontinuities and proposing a criterion for thermodynamic equilibrium.

Contribution

It clarifies the role of boundary terms in the model with smeared instantons and introduces a simple condition to determine equilibrium points.

Findings

Boundary terms are crucial at the infrared tip due to discontinuities.

A new criterion for thermodynamic equilibrium is proposed.

Insights into topological properties and current behavior in the model.

Abstract

We consider the Witten-Sakai-Sugimoto model in the approximation of smeared instantons at finite density via a homogeneous Ansatz, which is known to be discontinuous in order to be able to contain a nonvanishing baryon density. The discontinuity at the infrared tip of the bulk spacetime gives rise to subtleties of discarding boundary terms that are normally discarded in the literature. We propose a reason for discarding this boundary term, by scrutinizing the currents and topological properties of the model. Along the way, we find a very effective and simple condition to compute the point of thermodynamic equilibrium.