Exact solitons on noncommutative tori

TL;DR

This paper constructs exact soliton solutions on noncommutative tori within string field theory, linking projectors, gauge theories, and constant curvature connections to solve equations of motion precisely.

Contribution

It provides a detailed method for constructing exact solitons on noncommutative tori using projectors and gauge theory, advancing the understanding of solutions in string field theory.

Findings

Exact solitons are constructed on noncommutative tori.

Solutions correspond to projectors with constant curvature connections.

The approach links gauge theory to string field theory solutions.

Abstract

We construct exact solitons on noncommutative tori for the type of actions arising from open string field theory. Given any projector that describes an extremum of the tachyon potential, we interpret the remaining gauge degrees of freedom as a gauge theory on the projective module determined by the tachyon. Whenever this module admits a constant curvature connection, it solves exactly the equations of motion of the effective string field theory. We describe in detail such a construction on the noncommutative tori. Whereas our exact solution relies on the coupling to a gauge theory, we comment on the construction of approximate solutions in the absence of gauge fields.