From Feynman graphs to Witten diagrams

TL;DR

This paper explores extending Gopakumar's derivation of Witten diagrams from free to interacting large N quantum field theories, using Schwinger's proper time and loop organization.

Contribution

It introduces a method to generalize the derivation of Witten diagrams to interacting theories, specifically for a scalar field with $\

Findings

Two-point functions expressed as sums over boundary-to-boundary propagators in AdS.

Mass of bulk scalars related to the number of loops in Feynman diagrams.

Potential framework for connecting interacting quantum field theories with holographic duals.

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 $AdS_{d+1}$ with mass determined by $\ell$.