We study three dimensional conformal field theories described by U (N ) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ = N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |λ| = 1; the conformal theory does not exist for |λ| > 1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N . We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U (1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.

In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS 4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N ) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N ) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.

We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over "boundary excitations" of AdS 3 , which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.

We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in N = 4 super Yang-Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT 1 living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS 5 × S 5 ending on the line at the boundary and can be thought of as light fields propagating on the AdS 2 worldsheet. We use AdS/CFT techniques to compute the tree-level AdS 2 Witten diagrams describing the strong coupling limit of the fourpoint functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the "two-particle" operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang-Mills theory.

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We study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension ∆. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy δF = F UV − F IR . To describe the UV fixed point using the dual AdS 4 space we modify the boundary conditions on the spin s field in the bulk; this approach produces δF in agreement with the field theory calculations. If the spin s operator is a conserved current, then the fixed point is described by an induced parity invariant conformal spin s gauge theory. The low spin examples are QED 3 (s = 1) and the 3-d induced conformal gravity (s = 2). When the original CFT is that of N conformal complex scalar or fermion fields, the U (N ) singlet sector of the induced 3-d gauge theory is dual to Vasiliev's theory in AdS 4 with alternate boundary conditions on the spin s massless gauge field. We test this correspondence by calculating the leading term in δF for large N . We show that the coefficient of log N in δF is equal to the number of spin s − 1 gauge parameters that act trivially on the spin s gauge field. We discuss generalizations of these results to 3-d gauge theories including Chern-Simons terms and to theories where s is half-integer. We also argue that the Weyl anomaly a-coefficients of conformal spin s theories in even dimensions d, such as that of the Weyl-squared gravity in d = 4, can be efficiently calculated using massless spin s fields in AdS d+1 with alternate boundary conditions. Using this method we derive a simple formula for the Weyl anomaly a-coefficients of the d = 4 Fradkin-Tseytlin conformal higher-spin gauge fields. Similarly, using alternate boundary conditions in AdS 3 we reproduce the well-known central charge c = −26 of the bc ghosts in 2-d gravity, as well as its higher-spin generalizations.arXiv:1306.5242v3 [hep-th]

In this paper we simplify and extend previous work on three-point functions in Vasiliev's higher spin gauge theory in AdS 4 . We work in a gauge in which the space-time dependence of Vasiliev's master fields is gauged away completely, leaving only the internal twistor-like variables. The correlation functions of boundary operators can be easily computed in this gauge. We find complete agreement of the tree level three point functions of higher spin currents in Vasiliev's theory with the conjectured dual free O(N ) vector theory.

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.