Superconformal Symmetry in Three-dimensions

TL;DR

This paper explores the structure of superconformal symmetry in three-dimensional superspace, classifying transformations, identifying invariants, and deriving the general form of superconformal n-point functions.

Contribution

It provides a comprehensive classification of superconformal transformations and constructs the general form of superconformal correlators in three dimensions.

Findings

Superconformal group identified as OSp(N|2,R).

Superconformal invariants and correlators explicitly constructed.

Superconformally covariant differential operators discussed.

Abstract

Three-dimensional N-extended superconformal symmetry is studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz transformations, R-symmetry transformations and special superconformal transformations. Superconformal group is then identified with a supermatrix group, OSp(N|2,R), as expected from the analysis on simple Lie superalgebras. In general, due to the invariance under supertranslations and special superconformal transformations, superconformally invariant n-point functions reduce to one unspecified (n-2)-point function which must transform homogeneously under the remaining rigid transformations, i.e. dilations, Lorentz transformations and R-symmetry transformations. After constructing building blocks for superconformal correlators, we are able to identify all the superconformal invariants and obtain the general form of n-point functions. Superconformally covariant differential operators are also discussed.