This question arises in my project of finding the conformal field theory dual to the bosonic part of the Yang-Mills theory, i.e. non-supersymmetric large $N$ YM theory. Supersymmetry is a constant setup in most of AdS/CFT solutions, but I wonder if SUSY is absolutely necessary for the duality? By focusing on the bosonic spectrum in the correspondence and neglecting the fermions, can gauge/gravity duality be established without SUSY? (I'm not against SUSY, but calculations will be much easier without it.)


  1. http://arxiv.org/abs/hep-th/9901101, old paper from Klebanov and Tseytlin about non-SUSY CFT dual to type 0 string theory in AdS_5xS_5;

  2. http://arxiv.org/abs/hep-th/0207076, non-SUSY deformation of AdS/CFT showing correspondence without SUSY;

  3. http://arxiv.org/abs/0806.4068, non-SUSY CFT dual to 11D gravity M-theory (ABJM)

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    $\begingroup$ Hmm, your project is to find the gravity dual of pure YM? And after that, you collect the million dollar prize? $\endgroup$ – Thomas Sep 21 '18 at 16:08
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    $\begingroup$ "calculations will be much easier without it" .. What sort of calculations? Sometimes susy is all that makes a calculation possible. $\endgroup$ – Mitchell Porter Sep 21 '18 at 22:18
  • $\begingroup$ Certainly not the gravity dual to pure YM. Due to the flat direction of YM and therefore divergent partition function, I think there is no dual gravity. However, the YM with extra terms such as Lagrange multipliers might be doable when YM is regulated. The calculations in my mind are like t'Hooft's old computations in the matrix model. These are much easier without pfaffian, even numerically calculable with Monte Carlo methods. $\endgroup$ – whitejet Sep 24 '18 at 17:48
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    $\begingroup$ As far as I understand, SUSY is important in the duality mostly due to 3 aspects: 1) It naturally creates a parametrically large gaps in the operator spectrum. 2) It stabilizes the duality. 3) Practically, SUSY makes computations easier on both sides. 1) 2) are crucial whereas 3) is for convenience. $\endgroup$ – user110373 Oct 19 '18 at 3:56
  • $\begingroup$ For 1), I don't know if there is a large gap in the regulated YM until the further calculation is done, but a gap, potentially enlarged by quantum corrections, is observed in SYM matrix model in 1401.2020. To consider a proper standard model, I agree SUSY is necessary but maybe not so crucial for the duality? For 2), stabilization is supported by the regulator, i.e. the Lagrange multipliers, in the matrix YM model, see 1510.05779. $\endgroup$ – whitejet Oct 20 '18 at 14:43

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