Reflection Positivity and Levin-Wen Models

Arthur Jaffe Harvard University, Cambridge, MA 02138, United States of America Zhengwei Liu Harvard University, Cambridge, MA 02138, United States of America

Mathematical Physics arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.22004

Expositiones Mathematicae, 38, (2), 202-216, 2020.6
We give a transparent algebraic formulation of our pictorial approach to the reflection positivity (RP), that we introduced in a previous paper. We apply this quantization to the 2+1 Levin–Wen model to obtain 1+1 anyonic/quantum spin chain theory on the boundary, possibly entangled in the bulk. The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection positivity in terms of pictures. Here we give a transparent algebraic formulation of our pictorial approach. We use insights from this translation to establish the reflection positivity property for the fashionable Levin–Wen models with respect both to vacuum and to bulk excitations. We believe these methods will be useful for understanding a variety of other problems.
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@inproceedings{arthur2020reflection,
  title={Reflection Positivity and Levin-Wen Models},
  author={Arthur Jaffe, and Zhengwei Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707154544004964570},
  booktitle={Expositiones Mathematicae},
  volume={38},
  number={2},
  pages={202-216},
  year={2020},
}
Arthur Jaffe, and Zhengwei Liu. Reflection Positivity and Levin-Wen Models. 2020. Vol. 38. In Expositiones Mathematicae. pp.202-216. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707154544004964570.
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