Ran Yacoby

The N = 8 superconformal bootstrap in three dimensions

A bstractWe analyze the constraints imposed by unitarity and crossing symmetry on the four-point function of the stress-tensor multiplet of N=8

The \( \mathcal{N}=8 \) superconformal bootstrap in three dimensions

\mathcal{N}=8

Bounds on \( \mathcal{N} \) = 1 superconformal theories with global symmetries

superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stress-tensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stress-tensor central charge. To make contact with known N=8

O(N)

\mathcal{N}=8

< d <

superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large N limit of ABJM theory and also by the free U(1) × U(1) ABJM theory.

6

A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge CT . We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.