Chiral Higher Spin Gravity

Abstract

We construct a candidate for the most general chiral higher spin theory with AdS${}_3$ boundary conditions. In the Chern-Simons language, on the left it has the Drinfeld-Sokolov reduced form, but on the right all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are $19$ functions. Despite this, we show that the resulting metric has the form of the "most general" AdS${}_3$ boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a ${\mathcal{W}}_3$ algebra on the left and an affine $sl(3{)}_k$ current algebra on the right, as desired. The metric and higher spin fields depend on all the $19$ functions. We compare our work with previous results in the literature.

v2: refs added, minor corrections

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Cited by in corpus (7)

• New boundary conditions for (extended) ${\mathrm{AdS}}_3$ supergravity
• Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $Ad{S}_3$ Supergravity
• $\mathcal{N}=(2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $Ad{S}_3$ supergravity with new boundaries
• Black hole solutions of three dimensional E${}_6$-gravity
• On the $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal holographic dictionary
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography
• Spin-3 fields in Mielke-Baekler gravity