N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density

Details N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density

2000-11-14

arxiv.org/abs/gr-qc/0011046v2

Phys.Rev. D63 (2001) 104021

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, Latex, some more discussions and new references added, some typos corrected, accepted for publication in Physical Re

Scientific paper

10.1103/PhysRevD.63.104021

We obtain N = 3 chiral supergravity (SUGRA) compatible with the reality condition by applying the prescription of constructing the chiral Lagrangian density from the usual SUGRA. The $N = 3$ chiral Lagrangian density in first-order form, which leads to the Ashtekar's canonical formulation, is determined so that it reproduces the second-order Lagrangian density of the usual SUGRA especially by adding appropriate four-fermion contact terms. We show that the four-fermion contact terms added in the first-order chiral Lagrangian density are the non-minimal terms required from the invariance under first-order supersymmetry transformations. We also discuss the case of higher N theories, especially for N = 4 and N = 8.

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