Ashtekar's Formulation for N=1,2 Supergravities as "Constrained" BF Theories

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概要

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• 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 two-form fields subject to an algebraic constraint. We extend this relation between Ashtekar's formalism and BF theories to N=1 and N=2 supergrabities. The relavant 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 privide topological sulutions 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 thiories breaks down to the symmetry under diffeomorphisms and right-supersymmetry transformations.

• 理論物理学刊行会の論文
• 1996-05-25

著者

• Ezawa K

  Kyoto Univ. Kyoto

• EZAWA Kiyoshi

  Department of Physics, Osaka University

関連論文

• Ashtekar's Formulation for N=1,2 Supergravities as "Constrained" BF Theories

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