Seiberg-Witten Monopole Equations on Noncommutative R^4

TL;DR

This paper demonstrates the existence of finite action solutions to noncommutative Seiberg-Witten monopole equations on R^4_ heta, contrasting the trivial solutions in the commutative case, and interprets these solutions as string theory branes.

Contribution

It introduces explicit solutions to noncommutative SW equations on R^4_ heta and proposes their interpretation as D-brane solitons in string theory.

Findings

Existence of smooth, finite energy solutions on noncommutative R^4_ heta.

Construction of explicit regular solutions with nonzero topological charge.

Interpretation of solutions as D-brane-like solitons in string theory.

Abstract

It is well known that, due to vanishing theorems, there are no nontrivial finite action solutions to the Abelian Seiberg-Witten (SW) monopole equations on Euclidean four-dimensional space R^4. We show that this is no longer true for the noncommutative version of these equations, i.e., on a noncommutative deformation R^4_\theta of R^4 there exist smooth solutions to the SW equations having nonzero topological charge. We introduce action functionals for the noncommutative SW equations and construct explicit regular solutions. All our solutions have finite energy. We also suggest a possible interpretation of the obtained solutions as codimension four vortex-like solitons representing D(p-4)- and anti-D(p-4)-branes in a Dp-anti-Dp brane system in type II superstring theory.