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- W2094266885 abstract "It was recently shown by Witten that B-type open topological string theory with the supertwistor space $mathbb{C}P^{3|4}$ 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 $mathcal{N}=4$ super-Yang–Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual $mathcal{N}$-extended SYM theory as the integrability of SYM fields on complex $(2|mathcal{N})$-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 $mathbb{C}P^{3|mathcal{N}}$ to the field equations of self-dual $mathcal{N}$-extended SYM theory in four dimensions is made explicit. Furthermore, we extend the picture to the full $mathcal{N}=4$ 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 $mathbb{C}P^{3|3}times mathbb{C}P^{3|3}$." @default.
- W2094266885 created "2016-06-24" @default.
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- W2094266885 date "2005-01-01" @default.
- W2094266885 modified "2023-09-25" @default.
- W2094266885 title "On supertwistors, the Penrose--Ward transform and $CN=4$ super-Yang--Mills theory" @default.
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- W2094266885 doi "https://doi.org/10.4310/atmp.2005.v9.n6.a2" @default.
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