Higher spinAdSd+1/CFTdat one loop

Abstract

Following [1], we carry out one loop tests of higher spin AdS d+1 /CFT d correspondences for d ≥ 2. The Vasiliev theories in AdS d+1 , which contain each integer spin once, are related to the U (N ) singlet sector of the d-dimensional CFT of N free complex scalar fields; the minimal theories containing each even spin once -to the O(N ) singlet sector of the CFT of N 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 AdS d+1 . In even d we compare the result with the O(N 0 ) correction to the a-coefficient of the Weyl anomaly; in odd d -with the O(N 0 ) correction to the free energy F on the d-dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of N free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in d dimensions. As explained in [1], this result may agree with the O(N ) singlet sector of the theory of N real scalar fields, provided the coupling constant in the higher spin theory is identified as G N ∼ 1/(N −1). Our calculations in even d are closely related to finding the regularized a-anomalies of conformal higher spin theories. In each even d we identify two such theories with vanishing a-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 d = 5 obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large N theory is dual to the Vasiliev theory in AdS 6 where the bulk scalar is quantized with the alternate boundary condition.

ABJ theory in the higher spin limit

“…5 In this paper, following refs. [17,20], we circumvent this problem by computing the one-loop free energy, which can be computed without the action as long as we know the spectrum, and by comparing it with the ABJ free energy. In specifying the spectrum, it is crucial to choose appropriate boundary conditions of the HS fields.…”

“…We first show the absence of the logarithmic divergences: for s ∈ Z + 1/2, we can rewrite the spectral zeta function ζ (∆,s) (z) as a sum of two terms 20) where…”

“…We adopt the regularization used in the analysis [20]. 14 This yields JHEP08 (2016)174 where we used (4.22) to find the second line.…”

“…one loop of the HS theory for the vector models at both UV and IR fixed points [17][18][19][20]. Meanwhile, the collective field method was applied to the vector models, elucidating how the HS theory can be directly reconstructed from the VM as well as providing a new perspective on the origin of the duality as a gauge phenomenon [21][22][23][24][25][26].…”

Holography as a gauge phenomenon in Higher Spin duality

“…A recent overview of the canonical formulation of the AdS/CFT map can be found in [31]. A covariant version is also possible and is seen to explain [20] some of the interesting one-loop results found in [32,33]. More complex Higher Spin correspondences involving conformal theories in 2d are also of high interest [16,28].…”