On eleven-dimensional supergravity and Chern–Simons theory Original Research Article

We probe in some depth into the structure of eleven-dimensional, image-based Chern–Simons supergravity, as put forward by Troncoso and Zanelli (TZ) in 1997. We find that the TZ Lagrangian may be cast as a polynomial in image, where l is a length, and compute explicitly the first three dominant terms. The term proportional to image turns out to be essentially the Lagrangian of the standard 1978 supergravity theory of Cremmer, Julia and Scherk, thus establishing a previously unknown relation between the two theories. The computation is nontrivial because, when written in a sufficiently explicit way, the TZ Lagrangian has roughly one thousand non-explicitly Lorentz-covariant terms. Specially designed algebraic techniques are used to accomplish the results.