Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions

TL;DR

This paper provides an exact analytic solution for a strongly coupled gauged tensor model in quantum mechanics, revealing eigenvalues, eigenstates, and signs of chaos, advancing understanding of such complex theories.

Contribution

It presents the first exact analytic solution for a specific strongly coupled gauged tensor model, including eigenvalues and eigenstates, with comparison to numerical results.

Findings

Eigenvalues match previous numerical results

Explicit eigenstates derived

Spectrum shows signs of chaos

Abstract

Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely the smallest colored tensor model due to Gurau and Witten that exhibits non-linearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of $N$, exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the gory details will appear in a companion paper.