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Twistors, harmonics and holomorphic Chern-Simons

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Abstract

We show that the off-shell \( \mathcal{N}=3 \) action of \( \mathcal{N}=4 \) super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator \( \overline{\partial} \) is constructed from a complex-real (CR) structure of harmonic space. We also show that the local spacetime operators can be written as a Penrose transform on the coset SU(3)/(U(1) × U(1)). We observe a strong similarity to ambitwistor space constructions.

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  1. ETH Zürich, Institut für theoretische Physik, Wolfgang Pauli Strasse 27, 8093, Zürich, Switzerland

    Burkhard U. W. Schwab & Cristian Vergu

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  1. Burkhard U. W. Schwab
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  2. Cristian Vergu
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Correspondence to Burkhard U. W. Schwab.

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ArXiv ePrint: 1301.1536

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Schwab, B.U.W., Vergu, C. Twistors, harmonics and holomorphic Chern-Simons. J. High Energ. Phys. 2013, 46 (2013). https://doi.org/10.1007/JHEP03(2013)046

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