On eleven-dimensional Supergravity and Chern-Simons theory

TL;DR

This paper explores the structure of eleven-dimensional Chern-Simons supergravity, revealing a connection to standard supergravity through explicit polynomial expansion and advanced algebraic techniques.

Contribution

It demonstrates that the TZ Chern-Simons supergravity Lagrangian can be expanded as a polynomial in 1/l, linking it to the classic 1978 supergravity theory.

Findings

The Lagrangian is a polynomial in 1/l with explicit terms computed.

The 1/l^9 term matches the standard supergravity Lagrangian.

Advanced algebraic methods are used to handle complex Lorentz-covariant terms.

Abstract

We probe in some depth into the structure of eleven-dimensional, osp(32|1)-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 1/l, where l is a length, and compute explicitly the first three dominant terms. The term proportional to 1/l^9 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.