Interacting systems and wormholes

TL;DR

This paper explores tripartite quantum systems with cross-coupled quantum field theories, revealing connections to Euclidean wormholes and analyzing their partition functions, correlators, and Lorentzian continuations.

Contribution

It introduces a class of tripartite systems with cross-coupled QFTs via a messenger theory, extending to higher dimensions, and links their properties to gravitational wormholes.

Findings

Partition functions suggest duality to Euclidean wormholes.

Cross correlators are consistent with gravitational calculations.

Lorentzian continuations show features similar to gravitational backgrounds.

Abstract

We consider a class of tripartite systems for which two $d$-dimensional QFTs are cross-coupled via a third $d+1$-dimensional "messenger" QFT. We analyse in detail the example of a pair of one-dimensional matrix quantum mechanics, coupled via a two-dimensional theory of the BF-type and compute its partition function and simple correlators. This construction is extendible in higher dimensions, using a Chern-Simons "messenger" theory. In all such examples, the exact partition function acquires a form, speculated to correspond to systems dual to Euclidean wormholes and the cross correlators are sufficiently soft and consistent with analogous gravitational calculations. Another variant of the tripartite system is studied, where the messenger theory is described by a non-self-interacting (matrix)-field, reaching similar conclusions. While the Euclidean theories we consider are perfectly consistent, the two possible analytic continuations into Lorentzian signature (messenger vs. boundary QFT directions) of the tripartite models, reveal physical features and "pathologies" resembling those of the expected Lorentzian gravitational backgrounds.