On melonic supertensor models

Chi-Ming Chang Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA 95616 U.S.A. Sean Colin-Ellerin Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA 95616 U.S.A. Mukund Rangamani Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA 95616 U.S.A.

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74014

Journal of High Energy Physics, 2018, (157), 2018.10
We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large N limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for SL(2, ℝ) wavefunctions for fermionic excitations.
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@inproceedings{chi-ming2018on,
  title={On melonic supertensor models},
  author={Chi-Ming Chang, Sean Colin-Ellerin, and Mukund Rangamani},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702141815244594510},
  booktitle={Journal of High Energy Physics},
  volume={2018},
  number={157},
  year={2018},
}
Chi-Ming Chang, Sean Colin-Ellerin, and Mukund Rangamani. On melonic supertensor models. 2018. Vol. 2018. In Journal of High Energy Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702141815244594510.
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