Non-planar Diagrams and Non-commutative Superspace in Dijkgraaf-Vafa theory

TL;DR

This paper explores the connection between non-commutative superspace in string theory and supermatrix models, providing a new derivation of Dijkgraaf-Vafa theory that includes non-planar diagrams influenced by graviphoton backgrounds.

Contribution

It introduces a novel derivation of Dijkgraaf-Vafa theory incorporating non-planar diagrams through non-commutative superspace and supermatrix models.

Findings

Holomorphic quantities are equivalent to reduced models in the commutative limit.

Non-planar diagrams contribute to the theory due to graviphoton effects.

The approach extends Dijkgraaf-Vafa theory to non-commutative settings.

Abstract

We consider the field theory on non-commutative superspace and non-commutative spacetime that arises on D-branes in Type II superstring theory with a constant self-dual graviphoton and NS-NS $B$ field background. $\N=1$ supersymmetric field theories on this non-commutative space (such theories are called $\N=1/2$ supersymmetric theories.) can be reduced to supermatrix models as in hep-th/0303210 \cite{KKM}. We take an appropriate commutative limit in these theories and show that holomorphic quantities in commutative field theories are equivalent to reduced models, including non-planar diagrams to which the graviphoton contributes. This is a new derivation of Dijkgraaf-Vafa theory including non-planar diagrams.