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Self-dual structure of conformal supergravity. (English) Zbl 0954.83019

Summary: On the basis of a unified definition of the dual operation and the (anti-)self-dual operation, the connections of the \(\text{su} (2,2|1)\) main cluster was used as the fundamental field variables to construct the self-dual Lagrangian of conformal supergravity. A Yang-Mills-like Lagrangian is obtained and a new gauge theory of supergravity is put forward. The spatial projects of its spin connection are Ashtekar variables.

MSC:

83E50 Supergravity
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T13 Yang-Mills and other gauge theories in quantum field theory
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