%0 Generic %1 Beccaria2013Partition %A Beccaria, Matteo %A Macorini, Guido %D 2013 %K ads3-cft2, higher-spin %T On the partition functions of higher spin black holes %U http://arxiv.org/abs/1310.4410 %X We reconsider black hole solutions of D = 3 higher-spin gravity in the \$hsłambdahsłambda\$ Chern-Simons formulation. A suitable generalisation of the BTZ black hole has a spin-3 chemical potential \$\alpha\$, and non-zero values of all the conserved charges associated with the asymptotic \$W\_ınftyłambda\$ symmetry. We extend the available perturbative expansion of the partition function to order \$O(\alpha^18)\$ for generic values of the \$łambda\$ parameter. The result matches the CFT prediction at \$łambda=0\$ and at \$łambda=1\$ where we provide the exact all-order expansion of the partition function. The perturbative series is then analysed in the interesting non-trivial limit \$łambda\toınfty\$ and we derive the exact analytical expressions of the partition function and the spin-4 charge in closed form as functions of \$\alpha\$. Also, the first subleading correction at large \$łambda\$ is shown to be simply related to the leading contribution.

@misc{Beccaria2013Partition, abstract = {We reconsider black hole solutions of D = 3 higher-spin gravity in the \$hs[\lambda]\oplus hs[\lambda]\$ Chern-Simons formulation. A suitable generalisation of the BTZ black hole has a spin-3 chemical potential \$\alpha\$, and non-zero values of all the conserved charges associated with the asymptotic \$\mathcal W\_\infty[\lambda]\$ symmetry. We extend the available perturbative expansion of the partition function to order \$\mathcal O(\alpha^{18})\$ for generic values of the \$\lambda\$ parameter. The result matches the CFT prediction at \$\lambda=0\$ and at \$\lambda=1\$ where we provide the exact all-order expansion of the partition function. The perturbative series is then analysed in the interesting non-trivial limit \$\lambda\to\infty\$ and we derive the exact analytical expressions of the partition function and the spin-4 charge in closed form as functions of \$\alpha\$. Also, the first subleading correction at large \$\lambda\$ is shown to be simply related to the leading contribution.}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Beccaria, Matteo and Macorini, Guido}, biburl = {https://www.bibsonomy.org/bibtex/24bedcee0f6e2bef1b4df4c77ddac5a94/acastro}, citeulike-article-id = {12726373}, citeulike-linkout-0 = {http://arxiv.org/abs/1310.4410}, citeulike-linkout-1 = {http://arxiv.org/pdf/1310.4410}, day = 16, eprint = {1310.4410}, interhash = {24a873e14451da5cfed4e61a4580e214}, intrahash = {4bedcee0f6e2bef1b4df4c77ddac5a94}, keywords = {ads3-cft2, higher-spin}, month = oct, posted-at = {2013-10-17 13:58:41}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{On the partition functions of higher spin black holes}}, url = {http://arxiv.org/abs/1310.4410}, year = 2013 }