# Fermionization and boundary states in 1+1 dimensions

### Submission summary

 As Contributors: Yunqin Zheng Preprint link: scipost_202107_00026v2 Date accepted: 2021-09-28 Date submitted: 2021-09-01 14:36 Submitted by: Zheng, Yunqin Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### Abstract

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.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

### List of changes

Equation (2.40) and footnote 10 are added.

### Submission & Refereeing History

Resubmission scipost_202107_00026v2 on 1 September 2021
Resubmission scipost_202107_00026v1 on 14 July 2021
Submission 2103.00746v1 on 19 March 2021

## Reports on this Submission

### Report

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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