[HEG] Spectral Form Factor of Gapped Random Matrix Systems

Who: Krishan Saraswat (UCSB)  Title: Spectral Form Factor of Gapped Random Matrix Systems
Abstract: We study the spectral form factor of random matrix models which exhibit a large number of degenerate ground states accompanied by a macroscopic gap in the spectrum. We demonstrate that in such systems the standard narrative involving the spectral form factor is modified in the presence of a parametrically large number of ground states. We demonstrate on general grounds that the spectral form factor is dominated by the disconnected contribution, even at arbitrarily late times. We also show that the subleading connected contribution can only depend on the non-degenerate sector. Using the Christoffel-Darboux kernel we analyze a number of example systems including N=2 JT supergravity and demonstrate the existence of damped oscillations in the form factor whose period is controlled by the size of the spectral gap. We also demonstrate that in such gapped systems the ramp in the connected form factor arises from a universal sine-kernel which emerges from the non-perturbative kernel as hbar goes to zero which is in agreement with gravitational calculations involving the wormhole. We conclude by discussing how the transition from ramp to plateau occurs based on the form of the emergent sine-kernel and give additional comments regarding the factorization puzzle in such systems.