Domain wall fermions in holography

Abstract

This thesis will cover the development of holographic domain wall models, inspired by implementations of chiral fermions on the lattice. Starting in the D3/D7 holo- graphic system, and solving the Dirac-Born-Infeld (DBI) action for the sinusoidal embedding of the probe sevenbranes, a spatially dependant, step-like mass term for quarks in the dual theory can be included. Where this mass profile sharply passes through zero, massless quarks are isolated on co-dimension one domain wall defects in the dual gauge theory. Development of the large mass limit, allows us to exam- ine fluctuations in the dimensionally reduced theory living on the domain walls. We show that the domain wall theory is capable of dynamically generating mass for the dimensionally reduced quarks, complete with a Gell-Mann-Oakes-Renner relation between the masses of quarks, and pseudoscalar mesons, indicating the spontaneous breaking of “chiral” symmetry. With the construction of the holo- graphic domain walls understood, we implement them on the field theory limit of the D5/D7 intersection. This system is holographically dual to a 4+1 dimensional theory of quarks in a 5+1 dimensional confining gauge background. The resulting domain wall theory consists of 3+1 dimensional quarks in a confining geometry, and posesses neither conformal symmetry, nor supersymmetry. We dub this model Domain Wall AdS/QCD, and present a numerical calculation of its spectrum of mesonic observables. By including a black hole in the geometry, we can examine the phase transitions of the model at finite temperature, and find that there is a second order meson-melting transition.

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