Exact Seiberg-Witten Map and Induced Gravity from Noncommutativity

TL;DR

This paper derives an exact Seiberg-Witten map linking ordinary and noncommutative gauge theories, revealing that noncommutativity can be interpreted as gauge field-induced spacetime geometry fluctuations.

Contribution

It provides a closed-form Seiberg-Witten map and demonstrates how noncommutative Maxwell theory corresponds to a metric-deformed spacetime, advancing understanding of noncommutativity as induced geometry.

Findings

Exact Seiberg-Witten map derived

Noncommutative Maxwell action interpreted as geometry fluctuation

Noncommutativity viewed as gauge field-induced spacetime deformation

Abstract

We find a closed form for Seiberg-Witten (SW) map between ordinary and noncommutative (NC) Dirac-Born-Infeld actions. We show that NC Maxwell action after the exact SW map can be regarded as ordinary Maxwell action coupling to a metric deformed by gauge fields. We also show that reversed procedure by inverse SW map leads to a similar interpretation in terms of induced NC geometry. This implies that noncommutativity in field theory can be interpreted as field dependent fluctuations of spacetime geometry, which genuinely realizes an interesting idea recently observed by Rivelles.