From Feynman graphs to Witten diagrams

Abstract

We investigate the possibility of generalizing Gopakumar's microscopic derivation [1] of Witten diagrams in large N free quantum field theory to interacting theories. For simplicity we consider a massless, matrix valued real scalar field with ${\Phi }^h$ interaction in d-dimensions. Using Schwinger's proper time formulation and organizing the sum over Feynman graphs by the number of loops $\ell$, we show that the two-point function can be expressed as a sum over boundary-to-boundary propagators of bulk scalars in $Ad{S}_{d+1}$ with mass determined by $\ell$.

Contribution to "A Life in Mathematical Physics: Conference in Honour of Tekin Dereli" (DERELI-FS-2021)