Geometric Actions for Lower-Spin Gravity

TL;DR

This paper derives the boundary action for Lower Spin Gravity, a bulk dual to WCFT, and uses it to compute one-loop partition functions, linking geometric actions to Warped Virasoro characters.

Contribution

It provides a Hamiltonian reduction of Lower Spin Gravity and identifies the boundary action as a geometric action on coadjoint orbits of the Warped Virasoro group.

Findings

Derived the boundary action as a geometric action on coadjoint orbits.

Computed one-loop contributions to the torus partition function.

Compared results with Warped Virasoro characters.

Abstract

We perform the Hamiltonian reduction of Lower Spin Gravity, the simplest bulk dual for a Warped Conformal Field Theory (WCFT), consisting in an $SL(2) \times U(1)$ Chern-Simons model. We identify the boundary action as the geometric action on coadjoint orbits of the Warped Virasoro group. We use this reduced action to compute one-loop contributions to the torus partition function and compare them to the Warped Virasoro characters.