$N=2$ Super-Weyl Symmetry, Super-Liouville Theory and Super-Riemannian Surfaces

TL;DR

This paper derives finite $N=2$ super-Weyl transformations, computes the super-Weyl anomaly in $N=2$ fermionic string theory, and introduces a new framework for $N=2$ super-Riemannian surfaces.

Contribution

It provides explicit finite forms of $N=2$ super-Weyl transformations and proposes a novel definition of $N=2$ super-Riemannian surfaces in superspace.

Findings

Finite form of $N=2$ super-Weyl transformations derived.

Super-Weyl anomaly computed using $N=2$ heat kernel expansion.

New $N=2$ super-Riemannian surface definition proposed.

Abstract

The finite form of the $N=2$ super-Weyl transformations in the chiral and twisted-chiral irreducible formulations of the two-dimensional $N=2$ superfield supergravity are found in $N=2$ superspace. The super-Weyl anomaly of the $N=2$ extended fermionic string theory is computed in terms of the $N=2$ superfields, by using a short time expansion of the $N=2$ chiral heat kernel. The super-Weyl invariant $N=2$ superconformal structure is introduced, and a new definition of the $N=2$ super-Riemannian surfaces is proposed.