  It is suggested that many-body quantum chaos appears as spontaneous symmetry
breaking of unitarity in interacting quantum many-body systems. It has been
shown that many-body level statistics, probed by the spectral form factor (SFF)
defined as $K(\beta,t)=\langle|{\rm Tr}\, \exp(-\beta H + itH)|^2\rangle$, is
dominated by a diffusion-type mode in a field theory analysis. The key finding
of this paper is that the "unitary" $\beta=0$ case is different from the $\beta
\to 0^+$ limit, with the latter leading to a finite mass of these modes due to
interactions. This mass suppresses a rapid exponential ramp in the SFF, which
is responsible for the fast emergence of Poisson statistics in the
non-interacting case, and gives rise to a non-trivial random matrix structure
of many-body levels. The interaction-induced mass in the SFF shares
similarities with the dephasing rate in the theory of weak localization and the
Lyapunov exponent of the out-of-time-ordered correlators.
