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Implications of Hidden \(\mathscr {N}=(0,1)\) Super-Symmetry in \(\mathscr {N}=(1,1),\,6D\) SYM Theory

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Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 (LT-XII/QTS-X 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 255))

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Abstract

Using the harmonic superfield description of \(\mathscr {N}=(1,1)\) SYM theory, the list of possible candidate counterterms with the canonical dimensions d \(=\) 6, 8 and 10 is derived from hidden \(\mathscr {N}=(0,1)\) supersymmetry. The \(d=6\) and \(d= 8\) counterterms are at least on-shell vanishing, that means the one- and two-loop UV finiteness of \(\mathscr {N}=(1,1)\) SYM theory. The explicit quantum calculations in fact demonstrate a stronger property of its off-shell one-loop finiteness.

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Notes

  1. 1.

    The maximal off-shell supersymmetry with 16 supercharges is attainable in the “pure spinor” superfield formalism [8], but here we limit our attention to the standard superspaces.

  2. 2.

    We use the term “hidden supersymmetry” for some historical reasons. Perhaps, “non-manifest” would be more appropriate.

  3. 3.

    This just means that the on-shell vanishing counterterms can be absorbed into the microscopic action by a field redefinition. No equations of motion are assumed for the involved (super)fields.

  4. 4.

    Some latest results along this line are published in [25, 26].

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Acknowledgements

I thank the organizers of the X International Symposium “Quantum Theory and Symmetries” and XII International Workshop “Lie Theory and Its Applications in Physics” (and particularly Vladimir Dobrev) for the kind hospitality in Varna. I am indebted to my collaborators G. Bossard, I. Buchbinder, B. Merzlikin, A. Smilga, K. Stepanyantz and B. Zupnik. A partial support from the RSF Grant No. 16-12-10306, the RFBR grant No. 15-02-06670, and a grant of the Heisenberg - Landau program is acknowledged.

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  1. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow Region, Russia

    Evgeny Ivanov

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Correspondence to Evgeny Ivanov .

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  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Ivanov, E. (2018). Implications of Hidden \(\mathscr {N}=(0,1)\) Super-Symmetry in \(\mathscr {N}=(1,1),\,6D\) SYM Theory. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2. LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 255. Springer, Singapore. https://doi.org/10.1007/978-981-13-2179-5_5

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