D3/D7 holographic Gauge theory and Chemical potential

TL;DR

This paper investigates the phase structure of N=2 supersymmetric Yang-Mills theory with flavor at finite temperature and in de Sitter space using holographic duality, revealing a phase transition related to quark density and chemical potential.

Contribution

It introduces a holographic model with D7 branes to analyze phase transitions in flavored gauge theories at finite temperature and in de Sitter space, identifying critical chemical potentials and phase diagrams.

Findings

Critical chemical potential coincides with effective quark mass at zero density.

Phase transition occurs between different D7 brane embeddings.

Phase diagrams are mapped in chemical potential-temperature and chemical potential-cosmological constant planes.

Abstract

N=2 supersymmetric Yang-Mills theory with flavor hypermultiplets at finite temperature and in the dS${}_4$ are studied for finite quark number density ($n_b$) by a dual supergravity background with non-trivial dilaton and axion. The quarks and its number density $n_b$ are introduced by embedding a probe D7 brane. We find a critical value of the chemical potential at the limit of $n_b=0$, and it coincides with the effective quark mass given in each theory for $n_b=0$. At this point, a transition of the D7 embedding configurations occurs between their two typical ones. The phase diagrams of this transition are shown in the plane of chemical potential versus temperature and cosmological constant for YM theory at finite temperature and in dS${}_4$ respectively. In this phase transition, the order parameter is considered as $n_b$. % and the critical value of the chemical potential This result seems to be reasonable since both theories are in the quark deconfinement phase.