Baby universe operators in the ETH matrix model of double-scaled SYK

Abstract

We consider the baby universe operator ${\mathcal{B}}_a$ in the double-scaled SYK (DSSYK) model, which creates a baby universe of size $a$. We find that ${\mathcal{B}}_a$ is written in terms of the transfer matrix $T$, and vice versa. In particular, the identity operator on the chord Hilbert space is expanded as a linear combination of ${\mathcal{B}}_a$, which implies that the disk partition function of DSSYK is written as a linear combination of trumpets. We also find that the thermofield double state of DSSYK is generated by a pair of baby universe operators, which corresponds to a double trumpet. This can be thought of as a concrete realization of the idea of ER=EPR.

14 pages; v2: title changed, minor corrections

Cited by in corpus (1)

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