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 |