Solitons in Open N=2 String Theory

TL;DR

This paper investigates soliton solutions in open N=2 string theory, revealing localized three-branes, their superpositions, and smooth intersections, with implications for the theory's non-perturbative structure.

Contribution

It provides the first analysis of soliton solutions in the WZW_4 model related to open N=2 strings, demonstrating localized branes and their superpositions in split signature.

Findings

One-soliton solutions are localized on three-dimensional hyperplanes.

Multi-soliton solutions exhibit a nonlinear superposition behavior.

Energy densities of two-solitons are smooth with no singularities.

Abstract

The open N=2 string theory is defined on the four-dimensional space-time with the split signature (+,+,-,-). The string field theory action of the open N=2 string theory is described by the four-dimensional Wess-Zumino-Witten (WZW_4) model. Equation of motion of the WZW_4 model is the Yang equation which is equivalent to the anti-self-dual Yang-Mills equation. In this paper, we study soliton-type classical solutions of the WZW_4 model in the split signature by calculating the action density of the WZW_4 model. We find that the action density of the one-soliton solutions is localized on a three-dimensional hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently, some kind of three-branes in the open N=2 string theory. We also prove that in the asymptotic region of the space-time, the action density of the n-soliton solutions is a ``nonlinear superposition'' of n one-solitons. This suggests the existence of intersecting n three-branes in the N=2 strings. Finally we make a reduction to a (1+2)-dimensional real space-time to calculate energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.