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.

中文翻译：

---

测量张量模型的完整解

基于 arXiv:1706.05364 中引入的策略，我们为最简单的非线性 ($n=2, d=3$) 测量的 Gurau-Witten 张量模型的所有单线态特征值和特征值提供了精确的解析表达式。这完全解决了理论。在合适的约定中，基态特征值为 $-2\sqrt{14}$。这与通过计算机上的蛮力对角化获得的非测量模型中基态能量的结果相匹配。我们发现规范理论中剩余的简并性仅部分由其已知的离散对称性解释，表明系统中存在先前未识别的“隐藏”全局对称性。我们讨论了光谱形状因子、混沌的开始以及使用 $SO(n)$ 和 $O(n)$ 测量的理论之间的区别。我们的结果提供了 0+1 维非线性规范理论的完整解析解，尽管特定值为 $N$。本文的主要结果总结在随附信 arXiv:1802.02502 中。