Wormholes without averaging

TL;DR

This paper investigates the persistence of wormhole solutions in the SYK model with fixed couplings, revealing the emergence of new 'half-wormhole' saddles that are crucial for factorization but vanish upon averaging.

Contribution

It demonstrates that wormholes persist without averaging and introduces 'half-wormholes' as new saddle points, clarifying their role in factorization.

Findings

Wormhole saddles persist with fixed couplings.

Half-wormholes appear as new saddle points.

Half-wormholes are essential for factorization and vanish after averaging.

Abstract

After averaging over fermion couplings, SYK has a collective field description that sometimes has "wormhole" solutions. We study the fate of these wormholes when the couplings are fixed. Working mainly in a simple model, we find that the wormhole saddles persist, but that new saddles also appear elsewhere in the integration space -- "half-wormholes." The wormhole contributions depend only weakly on the specific choice of couplings, while the half-wormhole contributions are strongly sensitive. The half-wormholes are crucial for factorization of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind.