Resummation of scalar correlator in higher spin black hole background

Abstract

We consider the proposal that predicts holographic duality between certain 2D minimal models at large central charge and Vasiliev 3D higher spin gravity with a single complex field. We compute the scalar correlator in the background of a higher spin black hole at order $\mathcal{O}({\alpha }^5)$ in the chemical potential $\alpha$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra $\mbox{hs}[λ]$ parameter $\lambda$ and for the scalar in three different representations. We then study the perturbative data in the large $\lambda$ limit and discover remarkable regularities. This leads to formulate a closed formula for the resummation of the leading and subleading terms that scale like $\mathcal{O}({\alpha }^n{\lambda }^{2n})$ and $\mathcal{O}({\alpha }^n{\lambda }^{2n-1})$ respectively.

18 pages

References in corpus (3)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models

Cited by in corpus (5)

• Thermalization with chemical potentials, and higher spin black holes
• A new spin on entanglement entropy
• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
• Analysis of higher spin black holes with spin-4 chemical potential
• On scalar propagators of three-dimensional higher-spin black holes