Abstract
It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP^{3|4} as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual N-extended SYM theory as the integrability of super Yang-Mills fields on complex (2|N)-dimensional superplanes and demonstrate the equivalence of this description to Witten's formulation. The equivalence of the field equations of hCS theory on an open subset of CP^{3|N} to the field equations of self-dual N-extended SYM theory in four dimensions is made explicit. Furthermore, we extend the picture to the full N=4 SYM theory and, by using the known supertwistor description of this case, we show that the corresponding constraint equations are (gauge) equivalent to the field equations of hCS theory on a quadric in CP^{3|3}xCP^{3|3}.
Original language | English |
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Pages (from-to) | 931-998 |
Number of pages | 68 |
Journal | Advances in Theoretical and Mathematical Physics |
Volume | 9 |
Issue number | 6 |
DOIs | |
Publication status | Published - Dec 2005 |