On N=2 strings and classical scattering solutions of self-dual Yang-Mills in (2,2) spacetime

TL;DR

This paper explores classical solutions of self-dual Yang-Mills in (2,2) spacetime, revealing non-trivial scattering phenomena that are confined and do not correspond to physical four-point scattering, aligning with the vanishing amplitudes in N=2 string theory.

Contribution

It provides explicit classical solutions for SDYM with SL(2,C), showing how they relate to scattering properties and the vanishing of four-point amplitudes in N=2 string theory.

Findings

Solutions correspond to kink collisions with non-zero phase shifts

Stress energy is confined to string-like regions in spacetime

Solutions do not represent physical four-point scattering

Abstract

Ooguri and Vafa have shown that the open N=2 string corresponds to self-dual Yang-Mills (SDYM) and also that, in perturbation theory, it has has a vanishing four particle scattering amplitude. We discuss how the dynamics of the three particle scattering implies that on shell states can only scatter if their momenta lie in the same self-dual plane and then investigate classical SDYM with the aim of comparing exact solutions with the tree level perturbation theory predictions. In particular for the gauge group SL(2,C) with a plane wave Hirota ansatz SDYM reduces to a complicated set of algebraic relations due to de Vega. Here we solve these conditions and the solutions are shown to correspond to collisions of plane wave kinks. The main result is that for a class of kinks the resulting phase shifts are non-zero, the solution as a whole is not pure gauge and so the scattering seems non-trivial. However the stress energy and Lagrangian density are confined to string like regions in the space time and in particular are zero for the incoming/outgoing kinks so the solution does not correspond to physical four point scattering.