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Twistors in Conformally Flat Einstein Four-Manifolds

Giampiero Esposito·Giuseppe Pollifrone
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Abstract

This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a supercovariant derivative operator. The analysis of supergauge transformations of primary and secondary potentials for spin 3/2 shows that the gauge freedom for massive spin-3/2 potentials is generated by solutions of the supertwistor equations. The supercovariant form of a partial connection on a non-linear bundle is then obtained, and the basic equation of massive secondary potentials is shown to be the integrability condition on super beta-surfaces of a differential operator on a vector bundle of rank three. Moreover, in the presence of boundaries, a simple algebraic relation among some spinor fields is found to ensure the gauge invariance of locally supersymmetric boundary conditions relevant for quantum cosmology and supergravity.

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Giampiero Esposito, Giuseppe Pollifrone. 1995-07-06. Twistors in Conformally Flat Einstein Four-Manifolds. https://doi.org/10.1142/s0218271896000291

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