Mass Generation and Symmetry Breaking in Chern-Simons Supergravity

with R = dW + WW . On the fermion ground state, it is generally taken from granted that the right hand side vanishes. The goal of this paper is to study this assumption in detail. Chern-Simons gravity was first introduced in [2] in three dimensions. It was then pointed out [1] that the same construction can be carried over to five dimensions. Poincare Chern-Simons supergravities were introduced in [3], and their anti-de Sitter extensions in [4]. It was conjectured in [4] and [5] that M-theory may be described by eleven-dimensional Chern-Simons supergravity. This idea has recently been reexamined in [6]. A possible mechanism relating the field content of standard and Chern-Simons supergravities was discussed in [7]. The dynamical structure of higher dimensional Chern-Simons theories and their associated current algebras was studied in [8, 9, 10]. See also [11] for other aspects of higherdimensional Chern-Simons theories. Let us start by recalling the meaning of the ChernSimons level k and its relation to Planck’s scale. In the purely gravitational sector, the gauge fieldW is expanded as