Factorization and complex couplings in SYK and in Matrix Models

A bstract We consider the factorization problem in toy models of holography, SYK and Matrix Models. In a theory with fixed couplings, we introduce fictitious ensemble averaging by inserting projector onto couplings. compute squared partition function find that at large N for typical choice couplings it can be approximated two terms: “wormhole” plus “pair linked half-wormholes”. This resolves problem. second, half-wormhole, term thought as over imaginary part SYK, this reproduces known results from different perspective. matrix model an arbitrary potential, propose form half-wormholes” contribution. GUE, check errors are indeed small hamiltonian. Our computation relies on result Brezin Zee correlator resolvents “deterministic random” matrices.