# Fermionization and boundary states in 1+1 dimensions

### Submission summary

 Authors (as Contributors): Yunqin Zheng
Submission information
Date accepted: 2021-09-28
Date submitted: 2021-09-01 14:36
Submitted by: Zheng, Yunqin
Submitted to: SciPost Physics
Ontological classification
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.

Published as SciPost Phys. 11, 082 (2021)

### 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 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

### 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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