Integrable structures in classical off-shell 10D supersymmetric Yang-Mills theory

TL;DR

This paper explores integrable structures in 10D supersymmetric Yang-Mills theory, developing methods to derive physical fields and equations from modified flatness conditions that simplify the superfield content while preserving the off-shell spectrum.

Contribution

It introduces group-algebraic techniques to analyze modified flatness conditions, identifying integrable superspace constraints that reduce superfield complexity without losing physical content.

Findings

Derived physical fields and equations of motion from superfield expansions.

Identified superspace constraints that simplify superfield content.

Connected geometric constraints to light-like ray truncations.

Abstract

The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness conditions were proposed, which are explicitly integrable (hep-th/9811108), and are based on the breaking of symmetry SO(9,1) -> SO(2,1)xSO(7). In this article, we investigate their physical content. To this end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the spectrum including the original Yang-Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter families of light-like rays.