Seiberg-Witten Map for Superfields on Canonically Deformed N=1, d=4 Superspace

TL;DR

This paper constructs Seiberg-Witten maps for superfields in deformed N=1, d=4 superspace, revealing compatibility issues with locality, chirality, and supersymmetry in Minkowski space, but finding solutions in Euclidean space under specific conditions.

Contribution

It introduces Seiberg-Witten maps for superfields in deformed superspace and demonstrates their properties and limitations in Minkowski and Euclidean settings.

Findings

Seiberg-Witten map incompatible with locality, chirality, and supersymmetry in Minkowski space.

Existence of local, chiral, and supersymmetric Seiberg-Witten map in Euclidean space with selfdual noncommutativity.

Existence of local, antichiral, and supersymmetric Seiberg-Witten map in Euclidean space with antiselfdual noncommutativity.

Abstract

In this paper we construct Seiberg-Witten maps for superfields on canonically deformed N=1, d=4 Minkowski and Euclidean superspace. On Minkowski superspace we show that the Seiberg-Witten map is not compatible with locality, (anti)chirality and supersymmetry at the same time. On Euclidean superspace we show that there exists a local, chiral and supersymmetric Seiberg-Witten map for chiral superfields if we take the noncommutativity parameter to be selfdual, and a local, antichiral and supersymmetric Seiberg-Witten map for antichiral superfields if we take the noncommutativity parameter to be antiselfdual, respectively.