Compact Picture in Extended Superconformal Field Theories

TL;DR

This paper extends the compact picture coordinate framework for superconformal field theories in four-dimensional spacetime, generalizing a complex conformal transformation that maps Minkowski space into a bounded complex domain.

Contribution

The authors develop an extension of the compact picture coordinates specifically for superconformal field theories in four dimensions, broadening the mathematical tools available for such theories.

Findings

Provides a generalized conformal transformation for superconformal theories.

Establishes a new coordinate framework for 4D superconformal field theories.

Facilitates analysis of superconformal theories using compact picture coordinates.

Abstract

There is a complex conformal transformation, which maps the $D$ - dimensional real Minkowski space on a bounded set in the $D$ - dimensional complex vector space. It generalizes the Cayley map from $D=1$ dimensions to higher space-time dimensions. This transformation provides a very convenient coordinate picture for Conformal Field Theories called compact picture. In this paper we extend the compact picture coordinates for superconformal field theories in four space-time dimensions.