2PI effective action for the SYK model and tensor field theories

TL;DR

This paper develops the 2PI effective action framework for the SYK model and tensor field theories, providing a bilocal reformulation that aids in understanding soft modes and holographic aspects.

Contribution

It introduces the 2PI formalism for these models, enabling bilocal reformulations without replicas and revealing a one-loop structure at fourth order in 1/N expansion.

Findings

2PI effective action reproduces bilocal reformulation for SYK without replicas

2PI formalism is essential for bilocal reformulation in tensor theories

Uncovered one-loop structure at fourth order in 1/N expansion

Abstract

We discuss the two-particle irreducible (2PI) effective action for the SYK model and for tensor field theories. For the SYK model the 2PI effective action reproduces the bilocal reformulation of the model without using replicas. In general tensor field theories the 2PI formalism is the only way to obtain a bilocal reformulation of the theory, and as such is a precious instrument for the identification of soft modes and for possible holographic interpretations. We compute the 2PI action for several models, and push it up to fourth order in the $1/N$ expansion for the model proposed by Witten in arXiv:1610.09758, uncovering a one-loop structure in terms of an auxiliary bilocal action.