Spinning flavour branes and fermion pairing instabilities

TL;DR

This paper investigates instabilities in rotating probe Dp-branes in AdS_5 x S^5, revealing conditions for fermion pairing and Cooper-like condensates at strong coupling, contrasting with zero coupling behavior.

Contribution

It identifies and analyzes fermion pairing instabilities in strongly coupled gauge theories via holography, introducing a new understanding of chemical potential effects on D-brane embeddings.

Findings

Threshold chemical potentials trigger instabilities.

Unstable modes favor fermion bilinear condensates.

Strong coupling correlators show poles indicating instabilities.

Abstract

We consider probe Dp-branes, p=3,5,7, in global AdS_5 x S^5, rotating along an internal direction in the S^5. These are dual to strongly interacting N=4 SYM on S^3 with massless fundamental flavours, in the presence of an R-symmetry chemical potential for flavour fermions. For massless, "AdS-filling" Dp-brane embeddings at zero temperature, we find an infinite set of threshold values of the chemical potential at which instabilities are triggered. The onset of instability is always preceded by metastability of the zero density state. From the onset values of the chemical potential, we infer that unstable directions favour a homogeneous condensate of a bilinear made from fermion harmonics, or Cooper pairing. We confirm this picture both numerically and analytically. The linearized analysis showing the appearance of instabilities involves a charged scalar in global AdS space coupled to a (large) constant background gauge potential. The resulting frequency space correlator of the fermion bilinear at strong coupling displays poles in the upper half plane. In contrast, the correlator at zero coupling exhibits Pauli blocking due to occupation of states below the Fermi level, but no instabilities. The end-point of the strong coupling instability is not visible in our setup.