Domain wall fermions on the brane

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 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 spatially 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 backreacted 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 multitrace prescription.

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ORCID for Nick Evans: orcid.org/0000-0002-3255-4388

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