Superalgebras of Dirac operators on manifolds with special Killing-Yano tensors

✍ Scribed by I.I. Cotăescu; M. Visinescu

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 250 KB
• Volume: 54
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200610331

✦ Synopsis

Abstract

We present the properties of new Dirac‐type operators generated by real or complex‐valued special Killing‐Yano tensors that are covariantly constant and represent roots of the metric tensor. In the real case these are just the so called complex or hyper‐complex structures of the Kählerian manifolds. Such a Killing‐Yano tensor produces simultaneously a Dirac‐type operator and the generator of a one‐parameter Lie group connecting this operator with the standard Dirac one. In this way the Dirac operators are related among themselves through continuous transformations associated with specific discrete ones. We show that the group of these continuous transformations can be only U(1) or SU(2). It is pointed out that the Dirac and Dirac‐type operators can form 𝒩 = 4 superalgebras whose automorphisms combine isometries with the SU(2) transformation generated by the Killing‐Yano tensors. As an example we study the automorphisms of the superalgebras of Dirac operators on Minkowski spacetime.