The definition of Neveu-Schwarz superconformal fields and uncharged superconformal transformations

TL;DR

This paper constructs Neveu-Schwarz superconformal field theories for any N using superfield formalism, generalizes key mathematical tools to superconformal spaces, and derives the algebraic structure and transformation rules of primary fields.

Contribution

It provides a unified superfield formalism for N-extended Neveu-Schwarz superconformal theories and generalizes contour integration and Taylor expansion to superconformal spaces.

Findings

Derived operator product expansions for stress-energy tensor and primary fields.

Established the algebraic structure of K_N superconformal algebras.

Noted the disappearance of the central extension term for N≥4.

Abstract

The construction of Neveu-Schwarz superconformal field theories for any N is given via a superfield formalism. We also review some results and definitions of superconformal manifolds and we generalise contour integration and Taylor expansion to superconformal spaces. For arbitrary N we define (uncharged) primary fields and give their infinitesimal change under superconformal transformations. This leads us to the operator product expansion of the stress-energy tensor with itself and with primary fields. In this way we derive the well-known commutation relations of the Neveu-Schwarz superconformal algebras K_N. In this context we observe that the central extension term disappears for N>=4 for the Neveu-Schwarz theories. Finally, we give the global transformation rules of primary fields under the action of the algebra generators.