Wormhole calculus without averaging from O(N)q-1 tensor model

The Sachdev-Ye-Kitaev (SYK) model has a wormholelike solution after averaging over the fermionic couplings in the nearly AdS2 space. Even when the couplings are fixed the contribution of these wormholes continues to exist and new saddle points appear which are interpreted as half-wormholes. In this paper, we will study the fate of these wormholes in a model without quenched disorder, namely, a tensor model with O(N)q-1 gauge symmetry whose correlation function and thermodynamics in the large N limit are the same as that of the SYK model. We will restate the factorization problem linked with the wormhole threaded Wilson operator, in terms of global charges or nontrivial cobordism classes associated with disconnected wormholes. Therefore for the partition function to factorize especially at short distances, there must exist certain topological defects which break the global symmetry associated with wormholes and make the theory devoid of global symmetries. We will interpret these wormholes with added topological defects as our half-wormholes. We will also comment on the late time behavior of the spectral form factor, particularly its leading and subleading order contributions coming from higher genus wormholes in the gravitational sector. Finally we will show how the other nontrivial saddles from half-wormhole dominate and give rise to unusual thermodynamics in the bulk sector due to nonperturbative effects.

Automated summary

This paper examines the fate of wormholes in a model without quenched disorder and discusses their role in the factorization problem. It also explores the relationship between wormholes and topological defects, as well as the impact of wormholes on the spectral form factor.