Spectrum of a Supersymmetric Color Superconductor

TL;DR

This paper investigates the spectrum of mesonic excitations in a supersymmetric color superconductor using holographic duality, revealing Goldstone modes, extra ungapped modes, and novel brane configurations for multiple flavors.

Contribution

It provides a detailed holographic analysis of mesonic spectra in a supersymmetric superfluid, uncovering new features for multiple flavors and unequal R-symmetry charges.

Findings

Identified non-relativistic, massless Goldstone modes.

Discovered extra ungapped modes unrelated to symmetry breaking.

Found D5-brane supertube configurations for multiple flavors.

Abstract

We have recently shown that the ground state of ${\cal N} = 4$, SU($N_{\rm{\tiny c}}$) super Yang--Mills coupled to $N_{\rm{\tiny f}} \ll N_{\rm{\tiny c}}$ flavors, in the presence of non-zero isospin and R-symmetry charges, is a supersymmetric, superfluid, color superconductor. The holographic description consists of $N_{\rm{\tiny f}}$ D7-brane probes in AdS$_5\times$S$^5$ with electric and instantonic fields on their worldvolume. These correspond to fundamental strings and D3-branes dissolved on the D7-branes, respectively. Here we use this description to determine the spectrum of mesonic excitations. As expected for a charged superfluid we find non-relativistic, massless Goldstone modes. We also find extra ungapped modes that are not associated to the breaking of any global symmetries but to the supersymmetric nature of the ground state. If the quark mass is much smaller than the scale of spontaneous symmetry breaking a pseudo-Goldstone boson is also present. We highlight some new features that appear only for $N_{\rm{\tiny f}}> 2$. We show that, in the generic case of unequal R-symmetry charges, the dissolved strings and D3-branes blow up into a D5-brane supertube stretched between the D7-branes.