Domain walls in noncommutative gauge theories, folded D-branes, and communication with mirror world

TL;DR

This paper constructs BPS domain walls in noncommutative gauge theories, interprets them as folded D-branes, and explores their potential role as a mirror world with phenomenological implications.

Contribution

It introduces explicit solutions for domain walls in noncommutative gauge theories and links them to folded D-branes, offering a new perspective on gauge theory vacua and mirror worlds.

Findings

Domain walls separate vacua with different gauge groups.

Folded D-branes can be realized as solutions of the Matrix model.

Possible phenomenological implications of the mirror world scenario.

Abstract

Noncommutative U(N) gauge theories at different N may be often thought of as different sectors of a single theory. For instance, U(1) theory possesses a sequence of vacua labeled by an integer parameter N, and the theory in the vicinity of the N-th vacuum coincides with the U(N) noncommutative gauge theory. We construct domain walls on noncommutative plane, which separate vacua with different gauge groups in gauge theory with adjoint scalar field. The scalar field has nonminimal coupling to the gauge field, such that the scale of noncommutativity is determined by the vacuum value of the scalar field. The domain walls are solutions of the BPS equations in the theory. It is natural to interprete the domain wall as a stack of D-branes plus a stack of folded D-branes. We support this interpretation by the analysis of small fluctuations around domain walls, and suggest that such configurations of branes emerge as solutions of the Matrix model in large class of pp-wave backgrounds with inhomogeneous field strength. We point out that the folded D-brane per se provides an explicit realization of the "mirror world" idea, and speculate on some phenomenological consequences of this scenario.