Manifest Supersymmetry in Non-Commutative Geometry

TL;DR

This paper demonstrates that supersymmetry can be manifest in non-commutative geometry by analyzing superstring dynamics with a B field, showing unaltered fermionic anti-commutation and extending the Moyal product in superspace.

Contribution

It provides a superspace formulation of non-commutative supersymmetric field theories, establishing how supersymmetry is preserved in such geometries.

Findings

Fermionic anti-commutation relations remain unmodified.

Unbroken supersymmetry algebra is derived on the D-brane.

Extension of Moyal product in superspace is formulated.

Abstract

We consider the open superstring ending on a D-brane in the presence of a constant NS-NS B field, using the Green-Schwarz formalism. Quantizing in the light-cone gauge, we find that the anti-commutation relations for the fermionic variables of superspace remain unmodified. We also derive the unbroken supersymmetry algebra living on the D-brane. This establishes how the Moyal product is extended in a superspace formulation of non-commutative field theories. The superfield formulation of non-commutative supersymmetric field theories is briefly considered.