Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories

TL;DR

This paper explores the exact Seiberg-Witten map in noncommutative field theories, revealing connections to deformation quantization, induced gravity, and topological invariants, with implications for D-brane physics and gauge theory classifications.

Contribution

It provides an exact Seiberg-Witten map for scalar fields and topological invariants, clarifying their relation to commutative theories and gravity in noncommutative settings.

Findings

Exact SW map for adjoint scalar fields consistent with D-brane couplings

Mapping of NC instanton K-theory classes to commutative second Chern classes

SW map between NC and commutative Chern-Simons terms

Abstract

We revisit the exact Seiberg-Witten (SW) map on Dirac-Born-Infeld actions, making a connection with the deformation quantization scheme. The picture on field dependent induced gravity from noncommutativity becomes more transparent in the context of deformation quantization. We also find an exact SW map for an adjoint scalar field, consistent with that deduced from RR couplings of unstable non-BPS D-branes. The dual description via the exact SW map can again be interpreted as the ordinary field theory coupling to gravity induced by gauge fields. Using the exact SW maps, we further discuss several aspects of topological invariants in noncommutative (NC) gauge theory. Especially, it is shown that the K-theory class on NC instantons is mapped to the usual second Chern class via exact SW map and it leads to an exact SW map between commutative and NC Chern-Simons terms.