A Lax Operator for $d=2$ $N=2$ Supergravity

Abstract

General relativity and supergravity become integrable systems after dimensional reduction to two spacetime dimensions. This means the equations of motion can be encoded in the flatness condition for a Lax operator. Nicolai and Warner found Lax operators for dimensionally reduced supergravity. They gave explicit formulas primarily for the case with $N=16$ supersymmetry in two dimensions (which corresponds to $N=8$ supergravity in four dimensions). In this note, we derive analogous results for the case with $N=2$ supersymmetry in two dimensions (which corresponds to $N=1$ supergravity in four dimensions). This is the simplest example of the general fact that supergravity becomes an integrable system after dimensional reduction to two dimensions.

23 pages

References in corpus (2)

• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Infinite-Dimensional Symmetries of Two-Dimensional Coset Models Coupled to Gravity