Higher Spin Gravity in $AdS_3$ and Folds on Fermi Surface

TL;DR

This paper explores new boundary conditions in higher spin gravity in AdS3, linking boundary dynamics to collective field theory and folded Fermi surfaces, revealing integrable structures and conserved charges.

Contribution

It introduces novel boundary conditions for higher spin gravity in AdS3 that connect boundary dynamics to collective field theory and classical folded Fermi surface models.

Findings

Boundary conditions relate higher spin fields to collective field theory.

Identification of classical folded Fermi surface dynamics with spin evolution.

Discovery of infinite conserved charges indicating integrability.

Abstract

In this paper, we introduce new sets of boundary conditions for higher spin gravity in $AdS_3$ where the boundary dynamics of spin two and other higher spin fields are governed by the interacting collective field theory Hamiltonian of Avan and Jevicki. We show that the time evolution of spin two and higher spin fields can be captured by the classical dynamics of folded fermi surfaces in the similar spirit of Lin, Lunin and Maldacena. We also construct infinite sequences of conserved charges showing the integrable structure of higher spin gravity (for spin 3) under the boundary conditions we considered. Further, we observe that there are two possible sequences of conserved charges depending on whether the underlying boundary fermions are non-relativistic or relativistic.