Topological Dilatonic Supergravity Theories

TL;DR

This paper develops a topological supergravity theory in two dimensions based on an extended super-Poincaré algebra, revealing a non-local structure in the fermionic sector.

Contribution

It introduces a novel central extension of the two-dimensional super-Poincaré algebra and constructs a corresponding topological gauge theory with unique non-local fermionic features.

Findings

Classical solutions for non-multiplet fields obtained

Topological supergravity exhibits non-local fermionic behavior

Extended algebra includes new internal symmetry and central charge

Abstract

We present a central extension of the $(m,n)$ super-Poincar\'e algebra in two dimensions. Besides the usual Poincar\'e generators and the $(m,n)$ supersymmetry generators we have $(m,n)$ Grassmann generators, a bosonic internal symmetry generator and a central charge. We then build up the topological gauge theory associated to this algebra. We can solve the classical field equations for the fields which do not belong to the supergravity multiplet and to a Lagrange multiplier multiplet. The resulting topological supergravity theory turns out to be non-local in the fermionic sector.