New Boundary Conditions for AdS3

TL;DR

The paper introduces novel chiral boundary conditions for AdS$_3$ gravity with matter, yielding a single right-moving U(1) Kac-Moody-Virasoro algebra with $c_R=\frac{3\ell}{2G}$ and a KM level that can change sign between vacuum and black-hole sectors, indicating ergosphere-like instabilities. It derives finite, integrable charges and shows the asymptotic symmetry algebra, both in metric and Chern-Simons formalisms, including a dual chiral Liouville description on the boundary and the constraints implementing the new BCs. The authors also demonstrate that these BCs arise naturally in warped AdS$_3$ in the zero-warp limit and analyze bulk KM representations as well as string-theory realizations, highlighting potential holographic duals and instability mechanisms. Together, the results offer a semiclassical framework for a chiral boundary sector of AdS$_3$ gravity with matter and point to new avenues for holography and stability analyses in warped geometries.

Abstract

New chiral boundary conditions are found for quantum gravity with matter on AdS3. The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with c_R = 3l/2G. The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped AdS3 in the limit that the warp parameter is taken to zero.