IJPAM: Volume 42, No. 2 (2008)
BF THEORIES ON SUPER TWISTOR SPACES
Department of Science and Mathematics
437 Peguot Ave., New London, CT 06320, USA
Abstract.In 2003, Witten[#!Witten2!#] introduced the twistor string which is a string theory in super Twistor space, . One of the key ideas behind the twistor string is holomorphic Chern-Simons theory. It is of interest to extend the idea of twistor strings and thus holomorphic Chern-Simons theory beyond to other spaces in twistor theory such as super ambitwistor spaces.
In this talk, we shall begin with an introduction to twistor and ambitwistor spaces.
We quickly review various results from twistor theory such as Penrose-Ward transforms. We also present various ideas from supergeometry which we will be needing. After a short introduction to Chern-Simons theory and its holomorphic analog, we discuss holomorpic Chern-Simons theory on
. BF theory, another topological gauge theory and its extension by A. Popov [#!Popov1!#] to holomorphic BF theory are reviewed. We also give its extension to complex supermanifolds. Finally, we investigate holomorphic BF theory on super ambitwistor spaces and the role of holomorphic and almost complex bundles in holomorphic Chern-Simons and BF theories.
Received: August 17, 2007
AMS Subject Classification: 32L25, 58A50
Key Words and Phrases: twistor, Chern-Simons, BF theory, supermanifolds, super Yang-Mills equations, supersymmetry
Source: International Journal of Pure and Applied Mathematics