Doubly Supersymmetric Geometric Approach for Heterotic String: from Generalized Action Principle to Exactly Solvable Nonlinear Equations

TL;DR

This paper develops a doubly supersymmetric geometric framework for heterotic strings across multiple dimensions, deriving exactly solvable nonlinear equations from a generalized action principle, advancing the understanding of supersymmetric string dynamics.

Contribution

It introduces a novel doubly supersymmetric geometric approach based on a generalized action principle for heterotic strings, leading to exact nonlinear equations.

Findings

Proves off-shell superdiffeomorphism invariance of the generalized action.

Constructs a doubly supersymmetric geometric formulation for heterotic strings.

Derives a supersymmetric generalization of the nonlinear Liouville equation for D=3 heterotic string.

Abstract

The previously proposed generalized action principle approach to supersymmetric extended objects is considered in some details for the case of heterotic string in $D=3, 4, 6 ~and~ 10$ space--time dimensions. The proof of the 'off--shell' superdiffeomorphism invariance of the generalized action is presented. The doubly supersymmetric geometric approach to heterotic string is constructed on the basis of generalized action principle (instead of the geometrodynamic condition, used for this previously). It is demonstrated that $D=3$ heterotic string is described by $n=(1,0)$ supersymmetric generalization of the nonlinear Liouville equation.