Worldsheets with Extended Supersymmetry

TL;DR

This paper studies the gauge symmetries and anomalies of worldsheets with extended local supersymmetry of arbitrary rank, introducing superfields that generalize Beltrami differentials and connecting BRST invariant actions across different supersymmetry ranks.

Contribution

It provides a comprehensive formulation of gauge symmetries, anomalies, and supermoduli for worldsheets with arbitrary extended supersymmetry, linking them to topological models.

Findings

Derived equations governing gauge symmetries and anomalies for arbitrary N

Constructed superfield generalizations of Beltrami differentials

Connected BRST invariant actions across different N values

Abstract

We determine the equations which govern the gauge symmetries of worldsheets with local supersymmetry of arbitrary rank $(N,N')$, and their possible anomalies. Both classical and ghost conformally invariant multiplets of the left or right sector are assembled into the components of a single $O(N)$-superfield. The component with ghost number zero of this superfield is the $N$-supersymmetric generalization of the Beltrami differential. In a Lagrangian approach, and after gauge-fixing, it becomes the super-moduli of Riemann surfaces coupled to local supersymmetry of rank $N$. It is also the source of all linear superconformal currents derived from ordinary operator product techniques. The interconnection between BRST invariant actions with different values of $N\geq 3$, and their possible link to topological 2D-gravity coupled to topological sigma models, are shown by straightforward algebraic considerations.