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arXiv · 1311.5450

Resummation of scalar correlator in higher spin black hole background

Matteo Beccaria·Guido Macorini
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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 $\mathcal O(α^{5})$ in the chemical potential $α$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra $\mbox{hs}[λ]$ parameter $λ$ and for the scalar in three different representations. We then study the perturbative data in the large $λ$ limit and discover remarkable regularities. This leads to formulate a closed formula for the resummation of the leading and subleading terms that scale like $\mathcal O(α^{n}λ^{2n})$ and $\mathcal O(α^{n}\,λ^{2n-1})$ respectively.

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Matteo Beccaria, Guido Macorini. 2013-11-21. Resummation of scalar correlator in higher spin black hole background. https://doi.org/10.1007/jhep02(2014)071

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