Alladi Ramakrishnan Hall

Holographic SYK Models

Gautam Mandal

TIFR, Mumbai

We discuss low energy modes of SYK-type models as coadjoint orbits of diffeomorphism group on a real line or a circle, also called the Virasoro group. The Kirillov action on such coadjoint orbits coincides with the two-dimensional quantum gravity action of Polyakov, which therefore emerges as a natural description of the low energy sector of SYK-type models. More specifically, we propose that the gravity dual is described by Polyakov action with appropriate boundary terms on asymptotically (near-)AdS2 spaces. We present some evidence for this proposal by showing that in the classical limit, the action reduces to an appropriate Schwarzian form which can be identified with that appearing in the field theory as a description of the low energy modes near the IR fixed point. We also discuss the low energy thermodynamics of our model and find qualitative agreement with SYK-type models.