2021/09/01 by Robert F. Penna, Penna, Robert F.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2109.00597
openalex publication_date 2021/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.