Complete Solution of a Gauged Tensor Model

Building on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for all the singlet eigenstates and eigenvalues of the simplest non-linear ($n=2, d=3$) gauged Gurau-Witten tensor model. This solves the theory completely. The ground state eigenvalue is $-2\sqrt{14}$ in suitable conventions. This matches the result obtained for the ground state energy in the ungauged model, via brute force diagonalization on a computer. We find that the leftover degeneracies in the gauged theory, are only partially accounted for by its known discrete symmetries, indicating the existence of previously unidentified "hidden" global symmetries in the system. We discuss the spectral form factor, the beginnings of chaos, and the distinction between theories with $SO(n)$ and $O(n)$ gaugings. Our results provide the complete analytic solution of a non-linear gauge theory in 0+1 dimensions, albeit for a specific value of $N$. A summary of the main results in this paper were presented in the companion letter arXiv:1802.02502.