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.
Highlights
Kaplan introduced the idea of domain wall fermions in [1] to address the challenging issue of including chiral fermions in lattice gauge theory simulations
We apply the ideas of domain wall fermions but in holography [2]
We are motivated by enlarging the holographic toolbox of methods to construct particular gauge theories with holographic descriptions, as well as the formal aspect of studying a new environment in holography
Summary
We restrict the equation of motion for the 3 þ 1d probe scalar, that describes this operator/source pair, to the domain wall locus and solve It provides a direct local measure of the quark condensate, and its phase should play the role of the Goldstone of the symmetry breaking. We again show that the U-shaped domain wall configurations reach down to only a minimum value of ρ (above the singularity scale) and that the holographic fields on the domain wall consistently describe chiral symmetry breaking and a Gell-Mann-Oakes-Renner relation. The magnetic field prefactor pushes ρmin of the U-shaped configurations to higher values for a given width, but ρmin still approaches zero as the width of the U increases to infinity We use this system as a comparator for domain wall theories, returning to it in plots and the discussion below
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