We demonstrate that a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS 4 admits boundary conditions that preserve N = 0, 1, 2, 3, 4 or 6 supersymmetries. In particular, we argue that the Vasiliev theory with U (M ) Chan-Paton and 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 × 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 = 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.

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.

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 combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counterterms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F -theorem and possibly a C-theorem in five-dimensional superconformal theories.