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On the instantons and the hypermultiplet mass of \( \mathcal{N} = {{2}^{ * }} \) super Yang-Mills on S 4

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Abstract

We show that the physical \( \mathcal{N} = {4} \) super Yang-Mills theory on a four-sphere with an arbitrary gauge group receives no instanton contributions, by clarifying the relation between the hypermultiplet mass and the equivariant parameters of the mass-deformed theory preserving \( \mathcal{N} = {2} \) supersymmetry. The correct relation also implies that \( \mathcal{N} = {4} \) superconformal Yang-Mills theory with gauge group SU(2) corresponds to Liouville theory on a torus with the insertion of a non-trivial operator, rather than the identity as have been claimed in the literature.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Takuya Okuda

  2. Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, USA

    Vasily Pestun

Authors
  1. Takuya Okuda
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  2. Vasily Pestun
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Correspondence to Takuya Okuda.

Additional information

ArXiv ePrint: 1004.1222

On leave of absence from ITEP, 117218, Moscow, Russia. (Vasily Pestun)

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Okuda, T., Pestun, V. On the instantons and the hypermultiplet mass of \( \mathcal{N} = {{2}^{ * }} \) super Yang-Mills on S 4 . J. High Energ. Phys. 2012, 17 (2012). https://doi.org/10.1007/JHEP03(2012)017

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  • DOI: https://doi.org/10.1007/JHEP03(2012)017

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