We demonstrate that a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS4 admits boundary conditions that preserve $\mathcal{N}=0,1,2,3,4$ or 6 supersymmetries. In particular, we argue that the Vasiliev theory with U(M) Chan–Paton and $\mathcal{N}=6$ boundary condition is holographically dual to the 2+1 dimensional U(N)_k × U(M)_{−k} ABJ theory in the limit of large N, k and finite M. In this system all bulk higher spin fields transform in the adjoint of the U(M) gauge group, whose bulk t'Hooft coupling is M/N. Analysis of boundary conditions in Vasiliev theory allows us to determine exact relations between the parity breaking phase of Vasiliev theory and the coefficients of two and three point functions in Chern–Simons vector models at large N. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS_4\times \mathbb {CP}^3, and that the non-Abelian Vasiliev theory at strong bulk 't Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev's higher spin particles held together by U(M) gauge interactions. This is illustrated by the thermal partition function of free ABJ theory on a two sphere at large M and N even in the analytically tractable free limit. In this system the traces or strings of the low temperature phase break up into their Vasiliev particulate constituents at a U(M) deconfinement phase transition of order unity. At a higher temperature of order $T=\sqrt{\frac{N}{M}}$ Vasiliev's higher spin fields themselves break up into more elementary constituents at a U(N) deconfinement temperature, in a process described in the bulk as black hole nucleation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Higher spin theories and holography'.

In this paper, we study a class of sphere and torus correlation functions in the W_N minimal model. In particular, we show that a large class of exact sphere three-point functions of W_N primaries, derived using affine Toda theory, exhibit large N factorization. This allows us to identify some fundamental particles and their bound states in the holographic dual, including light states. We also derive the torus two-point function of basic primaries, by directly constructing the relevant conformal blocks. The result can then be analytically continued to give the Lorentzian thermal two-point functions.

We study Vasiliev’s system of higher spin gauge fields coupled to massive scalars in AdS_3, and compute the tree level two and three point functions. These are compared to the large N limit of the W_N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.

We argue that a large class of N=2 Chern-Simons-matter theories in three dimensions have a continuous family of exact IR fixed points described by suitable quartic superpotentials, based on holomorphy. The entire family exists in the perturbative regime. A nontrivial check is performed by computing the 4-loop beta function of the quartic couplings, in the ’t Hooft limit, with a large number of flavors. We find that the 4-loop beta function can only deform the family of 2-loop fixed points, and does not change the dimension of this family. We further present an explicit computation of a perturbative correction to the Zamolodchikov metric on this space of three-dimensional superconformal field theories.

In this paper we derive refined Petersson/Kuznetsov trace formulae with prescribed local ramifications. The spectral side of these formulae are much shorter than the standard versions. We use them to study the first moment and the subconvexity bound of certain Rankin-Selberg L-function in a hybrid setting.