  We show that the low temperature phase of a conjugate pair of uncoupled,
quantum chaotic, nonhermitian systems such as the Sachdev-Ye-Kitaev (SYK) model
or the Ginibre ensemble of random matrices are dominated by replica symmetry
breaking configurations with a nearly flat free energy that terminates in a
first order phase transition. In the case of the SYK model, we show explicitly
that the spectrum of the effective replica theory has a gap. These features are
strikingly similar to those induced by wormholes in the gravity path integral
which suggests a close relation between both configurations. For a non-chaotic
SYK, the results are qualitatively different: the spectrum is gapless in the
low temperature phase and there is an infinite number of second order phase
transitions unrelated to the restoration of replica symmetry.
