Double Self-Dual and Anti-Self-Dual Structure of N=1 Supergravity

Details Double Self-Dual and Anti-Self-Dual Structure of N=1 Supergravity Double Self-Dual and Anti-Self-Dual Structure of N=1 Supergravity

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998gregr..30.1735c&link_type=ejournal

General Relativity and Gravitation, Volume 30, Issue 12, pp.1735-1748

Physics

6

Dirac Matrices, Self-Dual Action

Scientific paper

Using the Dirac matrices the double self-dual and anti-self-dual structure of N=1 supergravity is discussed. It is shown that the (anti-)self-dual part of the curvature does not consist of the (anti-)self-dual part of the connection alone, and the (anti-)self-dual part of the Lagrangian quadratic in the curvature consists of the (anti-)self-dual part of the curvature alone only when the Lagrangian does not include torsion terms if the torsion of the spacetime does not vanish. Such a new Lagrangian is constructed. It includes no Einstein-Hilbert term but its self-dual part contains an Ashtekar term.

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