Ashtekar's formulation for $N=1,2$ supergravities as "constrained" BF theories

Details Ashtekar's formulation for $N=1,2$ supergravities as "constrained" BF theories Ashtekar's formulation for $N=1,2$ supergravities as "constrained" BF theories

1995-11-07

arxiv.org/abs/hep-th/9511047v3

Prog.Theor.Phys. 95 (1996) 863-882

Physics

High Energy Physics

High Energy Physics - Theory

26 pages Latex (references added)

Scientific paper

10.1143/PTP.95.863

It is known that Ashtekar's formulation for pure Einstein gravity can be cast into the form of a topological field theory, namely the $SU(2)$ BF theory, with the B-fields subject to an algebraic constraint. We extend this relation between Ashtekar's formalism and BF theories to $N=1$ and $N=2$ supergravities. The relevant gauge groups in these cases become graded Lie groups of $SU(2)$ which are generated by left-handed local Lorentz transformations and left-supersymmetry transformations. As a corollary of these relations, we provide topological solutions for $N=2$ supergravity with a vanishing cosmological constant. It is also shown that, due to the algebraic constraints, the Kalb-Ramond symmetry which is characteristic of BF theories breaks down to the symmetry under diffeomorphisms and right-supersymmetry transformations.

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