From Feynman graphs to Witten diagrams

Abstract

We investigate the possibility of generalizing Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories. For simplicity we consider a massless, matrix valued real scalar field with φh interaction in d-dimensions. Using Schwinger's proper time formulation and organizing the sum over Feynman graphs by the number of loops l, we show that the two-point function can be expressed as a sum over boundary-to-boundary propagators of bulk scalars in AdS d+1 with mass determined by l. This manuscript is intended as a contribution to the festschrift of prof. Tekin Dereli's on the occasion of his 72nd birthday.1