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On twistors and conformal field theories from six dimensions. (English) Zbl 1280.81129

Summary: We discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view. Specifically, we present a detailed cohomological analysis, develop both Penrose and Penrose-Ward transforms, and analyse the corresponding contour integral formulae. We also give twistor space action principles. We then dimensionally reduce the twistor space of six-dimensional space-time to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, we also find a novel twistor space amongst these reductions, which turns out to be suitable for a twistorial description of self-dual strings. For these reduced twistor spaces, we explain the Penrose and Penrose-Ward transforms as well as contour integral formulae.{
©2013 American Institute of Physics}

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
81R25 Spinor and twistor methods applied to problems in quantum theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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