Light-cone Superstring Field Theory, pp-wave background and integrability properties

TL;DR

This paper demonstrates that the vertex coefficients in light-cone superstring field theory on a pp-wave background satisfy integrability equations, enabling the calculation of correlators and revealing underlying Toda lattice hierarchy structures.

Contribution

It establishes the connection between string field theory coefficients and Hirota equations of the Toda hierarchy, extending to the full hierarchy at least up to second order in the string mass.

Findings

Vertex coefficients satisfy Hirota equations for dispersionless Toda hierarchy.

Neumann coefficients relate to two-point functions in an associated quantum system.

Full Toda hierarchy relations hold up to second order in string mass 0.

Abstract

We show that the three strings vertex coefficients in light--cone open string field theory satisfy the Hirota equations for the dispersionless Toda lattice hierarchy. We show that Hirota equations allow us to calculate the correlators of an associated quantum system where the Neumann coefficients represent the two--point functions. We consider next the three strings vertex coefficients of the light--cone string field theory on a maximally supersymmetric pp--wave background. Using the previous results we are able to show that these Neumann coefficients satisfy the Hirota equations for the full Toda lattice hierarchy at least up to second order in the 'string mass' $\mu$.