Superextension n=(2,2) of the complex Liouville equation and its solution

TL;DR

This paper derives a new exactly solvable form of the n=(2,2) super-Liouville equation using nonlinear realization of local supersymmetry, connecting it to superstring models and including the complex Liouville equation.

Contribution

It introduces a novel form of the n=(2,2) super-Liouville equation via nonlinear realization, linking it to superstring theory and providing explicit solutions.

Findings

New exactly solvable super-Liouville equation form

Supercovariant constraints lead to string-like component equations

General solution derived from bosonic string solutions

Abstract

It is shown that the method of the nonlinear realization of local supersymmetry previously developed in framework of supergravity being applied to the n=(2,2) superconformal symmetry allows one to get the new form of the exactly solvable n=(2,2) super-Liouville equation. The general advantage of this version as compared with the conventional one is that its bosonic part includes the complex Liouville equation. We obtain the suitable supercovariant constraints imposed on the corresponding superfields which provide the set of the resulting system of component equations be the same as that in model of N=2, D=4 Green-Schwarz superstring. The general solution of this system is derived from the corresponding solution of the bosonic string equation.