Conical Defects in Higher Spin Theories

TL;DR

This paper investigates conical defect geometries in higher spin theories in AdS_3, identifying conditions for smooth solutions and linking them to specific states in dual conformal field theories, thus advancing holographic understanding.

Contribution

It demonstrates the existence of smooth conical defect solutions in SL(N) higher spin theories and connects these geometries to light primary states in minimal model W_N CFTs.

Findings

Certain deficit angles yield smooth geometries for N≥4.

These geometries can be interpreted as wormholes between AdS_3 spaces.

Spectrum of solutions matches light primaries in dual CFTs.

Abstract

We study conical defect geometries in the SL(N) Chern-Simons formulation of higher spin gauge theories in AdS_3. We argue that (for N\geq 4) there are special values of the deficit angle for which these geometries are actually smooth configurations of the underlying theory. We also exhibit a gauge in which these geometries can be viewed as wormholes interpolating between two distinct asymptotically AdS_3 spacetimes. Remarkably, the spectrum of smooth SL(N,C) solutions, after an appropriate analytic continuation, exactly matches that of the so-called "light primaries" in the minimal model W_N CFTs at finite N. This gives a candidate bulk interpretation of the latter states in the holographic duality proposed in [1].