AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields

TL;DR

This paper analyzes AdS/CFT with fundamental matter in the presence of pure-gauge Kalb-Ramond B fields, examining both magnetic and electric configurations on D7-brane probes in zero and finite temperature backgrounds. The magnetic case reveals a repulsive effect that stabilizes D7 embeddings and, above a critical field, triggers spontaneous chiral symmetry breaking and a discrete meson spectrum with a Goldstone mode; at finite temperature a magnetic field can eliminate the melted phase, expanding the regime of chiral symmetry breaking. The electric case introduces a singular shell where the DBI action vanishes, necessitating worldvolume gauge fields to maintain regularity, and yielding a Stark-like meson mass shift in the weak-field limit; embedding dynamics and phase structure become intricate, particularly at finite density where canonical and grand canonical ensembles diverge. Overall, the work elucidates how external Kalb-Ramond fields qualitatively alter brane embeddings, chiral dynamics, and meson spectra in strongly coupled gauge theories, with implications for holographic modeling of QCD-like matter under external fields.

Abstract

We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fields are turned on in the background, into which a D7 brane probe is embedded. First we consider the case of a magnetic field in two of the spatial boundary directions. We show that at finite temperature, i.e. in the AdS-Schwarzschild background, the B field has a stabilizing effect on the mesons and chiral symmetry breaking occurs for a sufficiently large value of the B field. Then we turn to the electric case of a B field in the temporal direction and one spatial boundary direction. In this case, there is a singular region in which it is necessary to turn on a gauge field on the brane in order to ensure reality of the brane action. We find that the brane embeddings are attracted towards this region. Far away from this region, in the weak field case at zero temperature, we investigate the meson spectrum and find a mass shift similar to the Stark effect.