Abstract
We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss the relation between the character integral representation and the Rindler-AdS thermal partition function.
Highlights
The conjectured dualities [1, 2] between free/critical CFTs in the U(N ) (or O(N )) fundamental representation and Vasiliev higher spin gravities in AdS have stimulated a lot of nontrivial tests
We show that the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character
We can conclude that the regularized one-loop partition function (with the UV regularization introduced by e− 4t in the original definition (2.5)) of a field in the massive representation of is log Zs,ν e−ν 2+u2 du √
Summary
The conjectured dualities [1, 2] between free/critical CFTs in the U(N ) (or O(N )) fundamental representation and Vasiliev higher spin gravities in AdS have stimulated a lot of nontrivial tests (for a recent review of the higher spin/CFT duality see [3]) These tests can be roughly divided into two classes: those that match bulk tree level three-point functions [4, 5] and those that match bulk one-loop free energy [6,7,8,9,10,11,12,13,14]. This difficulty was bypassed in [12, 13] where the authors, inspired by earlier works [11, 14], expressed the higher spin spectral zeta functions, cf. (2.4), as an integral transformation of the corresponding characters of the AdS isometry group and applied it to a large class of higher spin theories
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
