Conical Defects in Higher Spin Theories

TL;DR

This work analyzes conical defects in three-dimensional higher spin gravity formulated as SL($N$)$_ ext{R} \times$ SL($N$)$_ ext{R}$ Chern-Simons theory and shows that for $N\ge 4$ there exists a discrete, holonomy-trivial set of smooth defects with locally AdS metrics, which can be gauge-transformed into traversable wormholes. By examining both Lorentzian and Euclidean signatures, the authors establish a precise bulk-boundary correspondence: after analytic continuation $k\to-(N+1)$, the spectrum and higher spin charges of these smooth bulk solutions match the light primaries $(\Lambda,\Lambda)$ of the ${\cal W}_N$ minimal models (with full matching in the Euclidean theory). This provides a compelling bulk interpretation for these primaries in the Gaberdiel-Gopakumar duality and reveals a richer spectrum of solitonic states influencing the mass gap in higher spin gravity. The analysis also clarifies the role of falloff conditions, holonomy classifications, and non-principal embeddings, and highlights interesting questions about Wick rotations and the physical relevance of Euclidean smooth configurations.

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].