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Fermionization and boundary states in 1+1 dimensions

by Yoshiki Fukusumi, Yuji Tachikawa, Yunqin Zheng

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Yunqin Zheng
Submission information
Preprint Link: scipost_202107_00026v2  (pdf)
Date accepted: 2021-09-28
Date submitted: 2021-09-01 14:36
Submitted by: Zheng, Yunqin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry. In this note we determine how the boundary states are mapped under this correspondence. We also interpret this mapping as the fusion of the original boundary with the fermionization interface.

List of changes

Equation (2.40) and footnote 10 are added.

Published as SciPost Phys. 11, 082 (2021)

Reports on this Submission

Report 1 by Gerard Watts on 2021-9-27 (Invited Report)

  • Cite as: Gerard Watts, Report on arXiv:scipost_202107_00026v2, delivered 2021-09-26, doi: 10.21468/SciPost.Report.3574


I would again like to thank the authors for their reply.

I do disagree with the authors on the immediate interpretation of the breaking of the sign ambiguity that they have brought about by requiring $P^*_3 P_4 \geq 0$ (does it fix $P_3$ or $P_4$?) but they have now introduced a rationale for reducing the number of boundary states to match their expectations. It could perhaps be that their interpretation is related by duality to mine (although I have not yet worked this out), but I don't see anything will be gained by arguing the point here any more.

As a way to fix the boundary states for boundary conditions which have origins in a physical argument, the spin Cardy constraint seems fine. As a way to define and classify boundary conditions, it seems rather less good - but it is not being used for that here. In the context of this paper, I think it is fine.

So, I would like to thank the authors again for their many improvements and I am happy (despite my reservations) to recommend publication in this form.

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