Manifest superconformal covariance in six-dimensional (2,0) theory

TL;DR

This paper develops a superconformal formalism for the six-dimensional (2,0) theory, introducing a superfield on a supercone that transforms linearly under the superconformal group, enabling manifest covariance.

Contribution

It presents a superconformal generalization of Dirac's formalism, defining a superfield on a supercone that transforms linearly under the supergroup OSp(8*|4), and relates it to conventional superfields.

Findings

Superfield transforms linearly under superconformal group

Derived covariant constraints reducing to known differential equations

Established relationship between new superfield and conventional superfields

Abstract

A superconformal generalization of Dirac's formalism for manifest conformal covariance is presented and applied to the free (2,0) tensor multiplet field theory in six dimensions. A graded symmetric superfield, defined on a supercone in a higher-dimensional superspace is introduced. This superfield transforms linearly under the transformations of the supergroup OSp(8*|4), which is the superconformal group of the six-dimensional (2,0) theory. We find the relationship between the new superfield and the conventional (2,0) superfields in six dimensions and show that the implied superconformal transformation laws are correct. Finally, we present a manifestly conformally covariant constraint on the supercone, which reduces to the ordinary differential constraint for the superfields in the six-dimensional space-time.