Aspects of Noncommutative Scalar/Tensor Duality

TL;DR

This paper explores the duality between noncommutative scalar and tensor fields, deriving the Seiberg-Witten map and analyzing the resulting theories, including their gravity structures and dispersion relations.

Contribution

It provides the first-order Seiberg-Witten map for noncommutative tensor fields and investigates their dual scalar theories, revealing differences from the mapped scalar theories.

Findings

No emergent gravity structure in this setup

Off-shell dual scalar differs from Seiberg-Witten mapped scalar

Derived p-form generalization of the Seiberg-Witten map

Abstract

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in $\theta$. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order $\theta $ is also derived.