Eur. Phys. J. C, 84, 675 (2024)
Notes on wormhole cancellation and factorization
Peng Cheng1,2 and Pujian Mao1
1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China.
2 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, 222 South Tianshui Road, Lanzhou 730000, Gansu, China.
* p.cheng.nl@outlook.com
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.
