JT Gravity and the Ensembles of Random Matrix Theory

Understand

We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry.

• The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries.
• Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk.
• In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer "torsion." Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure.