Solitons in 4d Wess-Zumino-Witten models -- Towards unification of integrable systems --

TL;DR

This paper constructs soliton solutions in the 4d Wess-Zumino-Witten model, revealing their KP-type behavior, and explores their implications for integrable systems, string theory, and noncommutative extensions.

Contribution

It introduces explicit soliton solutions in the 4dWZW model and connects them to integrable systems, string theory, and noncommutative geometry, advancing the understanding of these models.

Findings

Soliton solutions behave as KP-type solitons with localized energy density.

One-soliton and multi-soliton solutions describe intersecting soliton walls with phase shifts.

The model relates to string field theory of open N=2 strings in split signature.

Abstract

We construct soliton solutions of the four-dimensional Wess-Zumino-Witten (4dWZW) model in the context of a unified theory of integrable systems with relation to the 4d/6d Chern-Simons theory. We calculate the action density of the solutions and find that the soliton solutions behave as the KP-type solitons, that is, the one-soliton solution has a localized action/energy density on a 3d hyperplane in 4-dimensions (soliton wall) and the n-soliton solution describes n intersecting soliton walls with phase shifts. We note that the Ward conjecture holds mostly in the split signature (+,+,-,-). Furthermore, the 4dWZW model describes the string field theory action of the open N=2 string theory in the four-dimensional space-time with the split signature and hence our soliton solutions would describe a new-type of physical objects in the N=2 string theory. We discuss instanton solutions in the 4dWZW model as well. Noncommutative extension and quantization of the unified theory of integrable systems are also discussed.