Superfield theory and supermatrix model

TL;DR

This paper explores the duality between superfield theories on noncommutative superspaces and supermatrix models, establishing an explicit isomorphism and analyzing the commutative limit where the duality persists, linking superfields to D-branes.

Contribution

It provides a systematic formulation of superfield theories on noncommutative superspaces and explicitly constructs the dual supermatrix model representation.

Findings

Established the isomorphism between star product superfield theories and supermatrix models.

Identified a fine-tuned commutative limit where duality remains valid.

Linked superfield dual particles to D-instantons and D0-branes in different dimensions.

Abstract

We study the noncommutative superspace of arbitrary dimensions in a systematic way. Superfield theories on a noncommutative superspace can be formulated in two folds, through the star product formalism and in terms of the supermatrices. We elaborate the duality between them by constructing the isomorphism explicitly and relating the superspace integrations of the star product Lagrangian or the superpotential to the traces of the supermatrices. We show there exists an interesting fine tuned commutative limit where the duality can be still maintained. Namely on the commutative superspace too, there exists a supermatrix model description for the superfield theory. We interpret the result in the context of the wave particle duality. The dual particles for the superfields in even and odd spacetime dimensions are D-instantons and D0-branes respectively to be consistent with the T-duality.