On eleven-dimensional Supergravity and Chern-Simons theory

Details On eleven-dimensional Supergravity and Chern-Simons theory On eleven-dimensional Supergravity and Chern-Simons theory

2011-03-11

arxiv.org/abs/1103.2182v4

Physics

High Energy Physics

High Energy Physics - Theory

v1: 16 pages, no figures. v2: updated references and minor corrections. v3: 10 pages, no figures. Paper fully rewritten; resul

Scientific paper

10.1016/j.nuclphysb.2011.10.012

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.

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