Notes on Wormhole Cancellation and Factorization

TL;DR

This paper explores how wormhole contributions in AdS/CFT can cancel each other, restoring bulk partition function factorization through phase mechanisms in JT gravity and SYK models.

Contribution

It introduces a novel mechanism for wormhole cancellation using phase factors, enabling bulk factorization in holographic models.

Findings

Wormhole contributions can cancel via complex phases.

Phase cancellation restores bulk partition function factorization.

Examples include JT gravity and SYK model demonstrating this mechanism.

Abstract

In AdS/CFT, partition functions of decoupled CFTs living on separate asymptotic boundaries factorize. However, the presence of bulk wormholes connecting different boundaries tends to spoil the factorization of the bulk partition function, which leads to a disagreement between the two sides. In this paper, we present two examples where wormhole contributions cancel each other in bulk partition function calculations, thus the bulk factorization can be realized. The first example is in 2-dimensional Jackiw-Teitelboim (JT) gravity, where the proposed way of realizing the cancellation resides in the extra complex phases associated with different wormholes. The phases arise due to the degenerate vacua structure. In the example of the Sachdev-Ye-Kitaev (SYK) model, the cancellation can be achieved due to the distribution of the wormhole saddles on a complex plane. The two examples demonstrate a way of realizing bulk partition function factorization by extending the Hilbert space and dressing wormhole saddles with extra phases.