Frobenius–Chern–Simons gauge theory. (4th January 2017) - Bonezzi, Roberto; Boulanger, Nicolas; Sezgin, Ergin; Sundell, Per
Abstract: Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z 2 -graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius–Chern–Simons model (FCS) that was proposed in (arXiv:1505.04957 ) as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z 2 -grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H ⊗ F . We give a new model of this type based on a twisting of C [ Z 2 × Z 4 ], which leads to self-dual complexified gauge fields on AdS 4 . If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of C [ ( Z 2 ) 3 ] that yields the original model, and the Clifford algebra C ℓ 2 n which provides an FCS formulation of the bosonic Konstein–Vasiliev model with gauge algebra h u ( 4 n − 1, 0 )   .