SYK Model in a Non-Gaussian disorder ensemble and emergent Coleman's mechanism

Abstract

We consider the case of the SYK model with non-gaussian disorder in the large $N$ limit. After obtaining the effective action, we derive the density of states and the free energy of the modified theory. We show that the non-gaussian disorder corresponds to a non-local Liouville theory, and non-minimally coupled 2D gravity action. It also provides a nice realization of Colemania - Coleman's idea from the 80s of generating a small Cosmological Constant. Finally, we also calculate out of time order correlation functions (OTOC) for the model.

35 pages and 2 figures. In the previous version, there was a mistake in the definition of the model with respect to the Hubbard-Stratonovich transformation. This has been corrected