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.

We bootstrap N=(1,0) superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming E_8 flavor group, we present universal bounds on the central charge C_T and the flavor central charge C_J . Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on C_J , and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS_7×S^4/Z_2.

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 propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three-dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

We prove that there does not exist any weak coupling limit in the space of superconformal field theories in five and six dimensions, based on an analysis of the representation theory of the corresponding superconformal algebras. Holographically, this implies that superstring theories on AdS6 and AdS7 do not admit tensionless limits. Finally, we discuss the implications of our result on the existence of an action for coincident M5-branes.