Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model

TL;DR

This paper constructs and analyzes resonance soliton solutions in the four-dimensional Wess-Zumino-Witten model on ultrahyperbolic space, revealing behaviors relevant to string theory and soliton classification.

Contribution

It introduces new resonance soliton solutions in the WZW$_4$ model, linking them to string theory objects and providing a framework for classifying ASDYM solitons.

Findings

Constructed multiple-pole and V-shape soliton solutions.

Demonstrated soliton annihilation and creation processes.

Connected the Cauchy matrix approach with binary Darboux transformation.

Abstract

We present two kinds of resonance soliton solutions on the Ultrahyperbolic space $\mathbb{U}$ for the G=U(2) Yang equation, which is equivalent to the anti-self-dual Yang-Mills (ASDYM) equation. We reveal and illustrate the solitonic behaviors in the four-dimensional Wess-Zumino-Witten (WZW$_4$) model through the sigma model action densities. The Yang equation is the equation of motion of the WZW$_4$ model. In the case of $\mathbb{U}$, the WZW$_4$ model describes a string field theory action of open N=2 string theories. Hence, our solutions on $\mathbb{U}$ suggest the existence of the corresponding classical objects in the N=2 string theories. Our solutions include multiple-pole solutions and V-shape soliton solutions. The V-shape solitons suggest annihilation and creation processes of two solitons and would be building blocks to classify the ASDYM solitons, like the role of Y-shape solitons in classification of the KP (line) solitons. We also clarify the relationship between the Cauchy matrix approach and the binary Darboux transformation in terms of quasideterminants. Our formalism can start with a simpler input data for the soliton solutions and hence might give a suitable framework for the classification of the ASDYM solitons.