Worldsheets with Extended Supersymmetry

Abstract

We determine the equations which govern the gauge symmetries of worldsheets with local supersymmetry of arbitrary rank $(N,N^{\prime })$, 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 $N\ge 3$, and their possible link to topological 2D-gravity coupled to topological sigma models, are shown by straightforward algebraic considerations.

15 pages, Latex. A section on the connection to topological action is added

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Cited by in corpus (4)

• Explaining the Pure Spinor Formalism for the Superstring
• Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region
• Covariant Map Between Ramond-Neveu-Schwarz and Pure Spinor Formalisms for the Superstring
• A Note on Consistent Anomalies