One loop tests of higher spin AdS/CFT

Abstract

Vasiliev's type A higher spin theories in AdS 4 have been conjectured to be dual to the U (N ) or O(N ) singlet sectors in 3-d conformal field theories with N -component scalar fields. We compare the O(N 0 ) correction to the 3-sphere free energy F in the CFTs with corresponding calculations in the higher spin theories. This requires evaluating a regularized sum over one loop vacuum energies of an infinite set of massless higher spin gauge fields in Euclidean AdS 4 . For the Vasiliev theory including fields of all integer spin and a scalar with ∆ = 1 boundary condition, we show that the regularized sum vanishes. This is in perfect agreement with the vanishing of subleading corrections to F in the U (N ) singlet sector of the theory of N free complex scalar fields. For the minimal Vasiliev theory including fields of only even spin, the regularized sum remarkably equals the value of F for one free real scalar field. This result may agree with the O(N ) singlet sector of the theory of N real scalar fields, provided the coupling constant in the Vasiliev theory is identified as G N ∼ 1/(N − 1). Similarly, consideration of the U Sp(N ) singlet sector for N complex scalar fields, which we conjecture to be dual to the husp(2; 0|4) Vasiliev theory, requires G N ∼ 1/(N + 1). We also test the higher spin AdS 3 /CF T 2 conjectures by calculating the regularized sum over one loop vacuum energies of higher spin fields in AdS 3 . We match the result with the O(N 0 ) term in the central charge of the W N minimal models; this requires a certain truncation of the CFT operator spectrum so that the bulk theory contains two real scalar fields with the same boundary conditions.

ABJ theory in the higher spin limit

“…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].…”

“…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.…”

“…These determinants can be explicitly computed by applying the techniques developed in [111][112][113]. To proceed, we first simplify (4.2) by using the result of Giombi and Klebanov for the type-A Vasiliev theory [17],…”

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].…”

“…The world line scheme that we have employed for the present considerations most directly concerns the quadratic level of the theory and also the one loop equivalences seen in direct calculations performed in [20,32] (see also [51]). The structure of gauges that we identify should in principle extend to the interacting case.…”