Large N saddle formulation of quadratic building block theories

Abstract

I develop a large N saddle point formulation for the broad class of “theories of quadratic building blocks”. Such theories are those in which the sums over internal indices are contained in quadratic building blocks, e.g., φ 2 = Σ a = 1 N φ a φ a . The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N.