Half-wormholes in SYK with one time point

Understand

In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao.

• Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a "wormhole" saddle plus a "pair of linked half-wormholes" saddle.
• It explains factorization of decoupled systems.
• Here, we derive an explicit formula for the half-wormhole contribution.