The matching problem has no small symmetric SDP

@article{Braun2017TheMP,
  title={The matching problem has no small symmetric SDP},
  author={G{\'a}bor Braun and Jonah Brown-Cohen and Arefin Huq and Sebastian Pokutta and Prasad Raghavendra and Aurko Roy and Benjamin Weitz and Daniel Zink},
  journal={Mathematical Programming},
  year={2017},
  volume={165},
  pages={643-662}
}
Yannakakis (Proceedings of the STOC, pp 223–228, 1988; J Comput Syst Sci 43(3):441–466, 1991. doi:10.1016/0022-0000(91)90024-Y) showed that the matching problem does not have a small symmetric linear program. Rothvoß (Proceedings of the STOC, pp 263–272, 2014) recently proved that any, not necessarily symmetric, linear program also has exponential size. In light of this, it is natural to ask whether the matching problem can be expressed compactly in a framework such as semidefinite programming… 
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