Color Superconductivity, Fermionic Quasinormal Modes in Reissner-Nordstr\"{o}m-anti-de Sitter Spacetimes and Supersymmetry

TL;DR

This paper explores supersymmetric structures in fermionic systems within Reissner-Nordström-anti-de Sitter spacetimes, revealing unbroken supersymmetry through fermionic zero modes and quasinormal modes, with implications for color superconductivity and gravitational backgrounds.

Contribution

It uncovers unbroken N=2 supersymmetry in fermionic systems related to color superconductors and AdS black holes, linking zero modes and quasinormal modes to supersymmetric algebra structures.

Findings

Unbroken supersymmetry in color superconductor zero modes.

Supersymmetric algebra structure in fermionic quasinormal modes.

Fredholm and non-Fredholm operators analyzed with indices.

Abstract

We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordstr\"{o}m-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric algebras. The unbroken supersymmetry in the later is guaranteed by the existence of fermionic quasinormal modes in the Reissner-Nordstr\"{o}m-anti-de Sitter background. In this case the operators are not Fredholm and regularized indices are deployed.