Abstract
Following S. Giombi and I. R. Klebanov, [J. High Energy Phys. 12 (2013) 068], we carry out one-loop tests of higher spin correspondences for . The Vasiliev theories in , which contain each integer spin once, are related to the singlet sector of the -dimensional CFT of free complex scalar fields; the minimal theories containing each even spin once—to the singlet sector of the CFT of free real scalar fields. Using analytic continuation of higher spin zeta functions, which naturally regulate the spin sums, we calculate one-loop vacuum energies in Euclidean . In even we compare the result with the correction to the coefficient of the Weyl anomaly; in odd —with the correction to the free energy on the -dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in dimensions. As explained in Giombi and Klebanov, this result may agree with the singlet sector of the theory of real scalar fields, provided the coupling constant in the higher spin theory is identified as . Our calculations in even are closely related to finding the regularized anomalies of conformal higher spin theories. In each even we identify two such theories with vanishing anomaly: a theory of all integer spins, and a theory of all even spins coupled to a complex conformal scalar. We also discuss an interacting UV fixed point in obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large theory is dual to the Vasiliev theory in where the bulk scalar is quantized with the alternate boundary condition.
- Received 14 February 2014
DOI:https://doi.org/10.1103/PhysRevD.89.084004
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