Holographic Roberge-Weiss Transitions II: Defect Theories and the Sakai-Sugimoto Model

TL;DR

This paper investigates phase transitions in holographic models with imaginary chemical potential, extending previous work to include defect theories and the Sakai-Sugimoto model, revealing Roberge-Weiss transitions and their properties.

Contribution

It introduces an extension of holographic models with imaginary chemical potential, analyzing phase diagrams and transition behaviors in defect and Sakai-Sugimoto models.

Findings

Roberge-Weiss transitions occur at high temperatures in these models.

Transitions between phases are first order, with triple points where Roberge-Weiss lines meet.

Pressure scaling differs between defect theories and the Sakai-Sugimoto model.

Abstract

We extend the work of Aarts et al., including an imaginary chemical potential for quark number into the Sakai-Sugimoto model and codimension k defect theories. The phase diagram of these models are a function of three parameters, the temperature, chemical potential and the asymptotic separation of the flavour branes, related to a mass for the quarks in the boundary theories. We compute the phase diagrams and the pressure due to the flavours of the theories as a function of these parameters and show that there are Roberge-Weiss transitions in the high temperature phases, chiral symmetry restored for the Sakai-Sugimoto model and deconfined for the defect models, while at low temperatures there are no Roberge-Weiss transitions. In all the models we consider the transitions between low and high temperature phases are first order, hence the points where they meet the Roberge-Weiss lines are triple points. The pressure for the defect theories scales in the way we expect from dimensional analysis while the Sakai-Sugimoto model exhibits unusual scaling. We show that the models we consider are analytic in \mu^2 when \mu^2 is small.