Domain Wall Fermions on the Brane

TL;DR

This paper investigates domain wall fermions in a holographic D3/D7 system, analyzing their condensation, mass generation, and chiral symmetry breaking phenomena, with implications for understanding strongly coupled fermionic systems.

Contribution

It introduces a novel holographic setup for domain wall fermions with spatially dependent mass terms, exploring their condensation and symmetry breaking mechanisms.

Findings

Condensation and mass generation analogous to D3/D5 systems.

Quark mass scales as inverse of domain width w.

Magnetic field does not induce chiral symmetry breaking.

Abstract

We study domain wall fermions and their condensation in the D3/probe D7 system. A spatially dependent mass term for the N=2 hypermultiplet can be arranged to isolate distinct two component fermions on two 2+1 dimensional domain walls. We argue that the system shows condensation/mass generation analogous to the D3/probe D5 anti-D5 system. The chiral condensate and pion mass can be directly computed on the domain wall. We provide evidence that these systems with the domains separated by a width w have a bare (current) quark mass that scales as 1/w when the spatial dependent mass is large. Adding a magnetic field does not induce chiral symmetry breaking between the separated domain wall fermions, but a similar phenomenological dilaton factor can be made strong enough to introduce spontaneous symmetry breaking. We show a Gell-Man-Oakes-Renner relation for the pions in that case and also for the case where the D7 probe is in a back-reacted dilaton flow geometry. The vacuum configurations can also be interpreted as having a spontaneously generated mass by a Nambu-Jona-Lasinio four fermion operator, depending on the choice of boundary conditions on fluctuations, according to Witten's multi-trace prescription.