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

A bstract We consider the baby universe operator $$ {\mathcal{B}}_a $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:math> in the double-scaled SYK (DSSYK) model, which creates a baby universe of size a . We find that $$ {\mathcal{B}}_a $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:math> 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 $$ {\mathcal{B}}_a $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:math> , 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.