Abstract
We compute the one-loop free energies of the type-Aℓ and type-Bℓ higher-spin gravities in (d + 1)-dimensional anti-de Sitter (AdSd+1) spacetime. For large d and ℓ, these theories have a complicated field content, and hence it is difficult to compute their zeta functions using the usual methods. Applying the character integral representation of zeta function developed in the companion paper [arXiv:1805.05646] to these theories, we show how the computation of their zeta function can be shortened considerably. We find that the results previously obtained for the massless theories (ℓ = 1) generalize to their partially-massless counterparts (arbitrary ℓ) in arbitrary dimensions.
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Basile, T., Joung, E., Lal, S. et al. Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities. J. High Energ. Phys. 2018, 132 (2018). https://doi.org/10.1007/JHEP07(2018)132
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DOI: https://doi.org/10.1007/JHEP07(2018)132