Instability of N=2 gauge theory in compact space with an isospin chemical potential

TL;DR

This paper studies the effects of an isospin chemical potential on N=2 super-Yang-Mills theory on a three-sphere at strong coupling, revealing instabilities and a novel scalar condensate formation via AdS/CFT.

Contribution

It demonstrates the first scalar condensation in this context and explores the spectrum crossover behavior, providing new insights into the phase structure at strong coupling.

Findings

Identifies an instability at high chemical potential.

Finds scalar, not vector, meson condensation as the first excitation.

Shows a spectrum crossover with temperature.

Abstract

We investigate N=2 super-Yang-Mills theory on a three sphere in the presence of an isospin chemical potential at strong coupling using the AdS/CFT correspondence. This system exhibits an instability for sufficiently large values of the chemical potential. In contrast to other related models, the first excitation to condense is not a vector meson but rather a scalar charged under the global SO(4) symmetry group. Furthermore, the spectrum of fluctuations exhibits an interesting cross-over behaviour as a function of the dimensionless temperature. We construct the new ground state of the non-linear theory.