Vector-like description of SU (2) matrix-valued quantum field theories

Abstract

The AdS/CFT correspondence asserts a duality between non-Abelian gauge theories and quantum theories of gravity, established by the value of the gauge coupling . Gerard t'Hooft found that the large N0 limit in non-Abelian Yang-Mills gauge theories results in a planar diagram simpli cation of the topological expansion. In this dissertation, SU(2) gauge theories are written in terms of vector models (making use of collective eld theory to obtain an expression for the Jacobian), a saddle point analysis is performed, and the large N limit taken. Initially this procedure is done for gauge theories dimensionally reduced on T4 and R T3, and then attempted for the full eld theory (without dimensional reduction). In each case this results in an expression for the non-perturbative propagator. A nite volume must be imposed to obtain a gap equation for the full eld theory; directives for possible solutions to this di culty are discussed.