On integrable structure of the null string in (anti-)de Sitter space

TL;DR

This work studies the integrable structure of the null (tensionless) string in (anti-)de Sitter space by deriving a Lax-pair representation on coset spaces and linking it to the tensile-string zero-curvature formulation. The authors develop a group-theoretic framework using Cartan forms and Maurer-Cartan equations to express the null-string dynamics via a Lax equation $\rho^i\nabla_i L-[L,M]=0$ with $L=\rho^i G^{Da'}_i M_{Da'}$ and $M=\rho^i G^{a'b'}_i M_{a'b'}$, and they present a phase-space (Hamiltonian) version of the Lax pair, showing its reduction to the null-string case in the tensionless limit. They further compare the null-string Lax structure with the standard tensile-string zero-curvature representation, deriving limiting relations where the tensile Lax components converge to the null-string form, and they propose a twistor interpretation of the group-variable formulation for AdS spaces. The results illuminate how integrable structures may persist in tensionless limits and provide a pathway to extending these insights to superstrings on AdS supercosets via twistor methods and group-theoretic variables.

Abstract

Presently integrability turned 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 considered is the limiting case of zero tension corresponding to null string. It is obtained the representation in the form of the Lax equation of null-string equations in (anti-)de Sitter space realized as coset manifold. Proposed is twistor interpretation of the Lagrangian of (null) string in anti-de Sitter space expressed in terms of group variables.