On Integrable Structure of Null String in (Anti-)de Sitter Space

TL;DR

This paper explores the integrable structure of null strings in (anti-)de Sitter space, deriving a Lax representation and proposing a twistor interpretation to simplify the complex superstring equations.

Contribution

It introduces a Lax equation formulation for null strings in (anti-)de Sitter space and offers a twistor-based interpretation, advancing understanding of integrability in simplified string models.

Findings

Derived Lax equation for null strings in (A)dS space

Proposed twistor interpretation of the string Lagrangian

Simplified the study of superstring integrability in limiting cases

Abstract

Presently integrability turned out to be the key property in the study of duality between superconformal gauge theories and strings in anti-de Sitter superspaces. Complexity of the study of integrable structure in string theory is caused by complicated dependence of background fields of the Type II supergravity multiplets, with which strings interact, on the superspace coordinates. This explains an interest to study of limiting cases, in which superstring equations simplify. In the present work, we considered the limiting case of zero tension corresponding to null string. The representation in the form of the Lax equation of null-string equations in (anti-)de Sitter space realized as a coset manifold is obtained. Proposed is twistor interpretation of the Lagrangian of (null) string in anti-de Sitter space expressed in terms of group variables.