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Duality between \( \mathcal{N}=5 \) and \( \mathcal{N}=6 \) Chern-Simons matter theory

Abstract

We provide evidences for the duality between \( \mathcal{N}=6\,U{(M)_4}\times U{(N)_{-4 }} \) Chern-Simons matter theory and \( \mathcal{N}=5\,O{{\left( {\widehat{M}} \right)}_2}\times U\,Sp{{\left( {2\widehat{N}} \right)}_{-1 }} \) theory for a suitable \( \widehat{M},\widehat{N} \) by working out the superconformal index, which shows perfect matching. For \( \mathcal{N}=5 \) theories, we show that supersymmetry is enhanced to \( \mathcal{N}=6 \) by explicitly constructing monopole operators filling in SO(6) R R-currents. Finally we work out the large N index of O(2N)2k × U Sp(2N)k and show that it exactly matches with the gravity index on AdS 4 × S 7 /D k , which further provides additional evidence for the duality between the \( \mathcal{N}=5 \) and \( \mathcal{N}=6 \) theory for k = 1.

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Correspondence to Jaemo Park.

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ArXiv ePrint: 1208.6085[hep-th]

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Cheon, S., Gang, D., Hwang, C. et al. Duality between \( \mathcal{N}=5 \) and \( \mathcal{N}=6 \) Chern-Simons matter theory. J. High Energ. Phys. 2012, 9 (2012). https://doi.org/10.1007/JHEP11(2012)009

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  • DOI: https://doi.org/10.1007/JHEP11(2012)009

Keywords

  • Duality in Gauge Field Theories
  • AdS-CFT Correspondence
  • Chern-Simons Theories