IJPAM: Volume 42, No. 2 (2008)


Andrew McHugh
Department of Science and Mathematics
Mitchell College
437 Peguot Ave., New London, CT 06320, USA
e-mail: mchugh_a@mitchell.edu

Abstract.In 2003, Witten[#!Witten2!#] introduced the twistor string which is a string theory in super Twistor space, ${\bf CP}^{3\vert 4}$. 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 ${\bf CP}^{3\vert 4}$ 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 ${\bf CP}^{3\vert 4}$. 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
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2