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Dualities for loop amplitudes of N = 6 Chern-Simons matter theory

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Abstract

In this paper we study the one- and two-loop corrections to the four-point amplitude of \( \mathcal{N}{ = 6} \) Chern-Simons matter theory. Using generalized unitarity methods we express the one- and two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the two-loop result is non-vanishing and matches with the Wilson loop computation. Furthermore, the two-loop correction takes the same form as the one-loop correction to the four-point amplitude of N = 4 super Yang-Mills. We discuss possible higher loop extensions of this correspondence between the two theories. As a side result, we extend the method of dimensional reduction for three dimensions to five dimensions where dual conformal symmetry is most manifest, demonstrating significant simplification to the computation of integrals.

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Authors and Affiliations

  1. Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan, ROC

    Wei-Ming Chen

  2. California Institute of Technology, Pasadena, CA, 91125, USA

    Wei-Ming Chen

  3. Department of Physics and Astronomy, UCLA, Los Angeles, CA, 90095-1547, USA

    Yu-tin Huang

  4. Kavli Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA, 93106-4030, USA

    Yu-tin Huang

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Chen, WM., Huang, Yt. Dualities for loop amplitudes of N = 6 Chern-Simons matter theory. J. High Energ. Phys. 2011, 57 (2011). https://doi.org/10.1007/JHEP11(2011)057

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