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Perturbative Gauge Theory as a String Theory in Twistor Space

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Abstract

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold

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  1. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Edward Witten

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  1. Edward Witten
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Communicated by M.R. Douglas

Dedicated to Freeman Dyson for his 80th birthday

Acknowledgement I am indebted to N. Berkovits for numerous helpful discussions of some of these ideas and pointing out a number of significant references, to F. Cachazo for extensive assistance with computer algebra, to L. Dixon for answering many queries about perturbative Yang-Mills theory, and to M. F. Atiyah and R. Penrose for mathematical consultations. This work was supported in part by NSF Grant PHY-0070928.

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Witten, E. Perturbative Gauge Theory as a String Theory in Twistor Space. Commun. Math. Phys. 252, 189–258 (2004). https://doi.org/10.1007/s00220-004-1187-3

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