Interacting systems and wormholes

TL;DR

<3-5 sentences high-level summary> The paper investigates tripartite quantum-field theories in which two d-dimensional boundary QFTs couple through a d+1-dimensional messenger theory, focusing on matrix-model realizations and higher-dimensional generalizations. It shows that integrating out the messenger yields a non-factorising but sectorally structured partition function, naturally aligning with Euclidean wormhole physics via a sum over sectors labeled by representations (or analogous data) and weighted by Casimir-like factors. The authors develop Hall-Littlewood polynomial techniques to compute exact partition functions and cross-boundary correlators, demonstrating UV-soft cross-correlations with no short-distance singularities, and analyze Lorentzian continuations that reveal pathologies depending on the analytic continuation. They further explore higher-dimensional messengers (Chern-Simons, BF theories) and simpler cross-coupled QFTs, highlighting how wormhole-like saddles may emerge or be suppressed, and discuss implications for holography, confinement, and connections to black-hole physics. The work provides a versatile framework for understanding factorisation vs. non-factorisation in holographic duals of wormholes and cosmologies, with potential D-brane realizations and broad generalizations to multi-boundary systems.

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.

Figures (2)

• Figure 1: The plots on the left are for $g = 1, m=1, M=10$. The plots on the right are for $g = 1, m=1, M=1$. The upper plots depict $G_{++}(x) = D_{+}^{-1}(x)$ (extra dimension is an infinite line), while the lower plots are for $G_{++}(x) = (D^I_{+})^{-1}(x)$ (extra dimension is a finite interval). The noise on the right side plots is in regions of large numerical error, but we can safely trust the complementary region, where the graph is smooth. We observe a violation of reflection positivity in the regime $m \simeq M$ (and for values of $x$ for which we have acceptable numerical error). This violation is also dependent on the parameter $g$ and increases for large $g$. The $G_{--}(x)$ correlators are found to be reflection positive in the regime of parameters that we could numerically analyse. The results are similar to the analytic results of the non-local model worm.
• Figure 2: The upper plots depict $G_{++}(x) = D_{+}^{-1}(x)$ (extra dimension is an infinite line). The upper left figure is for $g = 1, m=1, M=10$, showing the reflection positivity of the propagator, while the upper right is for $g = 1, m=1, M=1$, where it is not reflection positive. The lower left plot is for $G^I_{++}(x) = (D^I_{+})^{-1}(x)$ (extra dimension is a finite interval), while the lower right plot is for $G^I_{--}(x) = (D^I_{-})^{-1}(x)$ both for $g = 1, m=1, M=10$, where they used to be reflection positive in the case of Euclidean messenger propagation. We find relatively large noise and numerical error, since the integrand is highly oscillatory near the regions in which it diverges. We observe a clear violation of reflection positivity for the $G^I_{++}(x)$ propagator, in the interval where the curve is smooth, while in the case of the $G^I_{--}(x)$ the ratio error/value is large and we cannot safely draw a conclusion.