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M$_k$ models: the field theory connection

by T. Fokkema, K. Schoutens

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Submission summary

Authors (as registered SciPost users): Kareljan Schoutens
Submission information
Preprint Link:  (pdf)
Date submitted: 2017-06-21 02:00
Submitted by: Schoutens, Kareljan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


The M$_k$ models for 1D lattice fermions are characterised by ${\cal N}=2$ supersymmetry and by an order-$k$ clustering property. This paper highlights connections with quantum field theories (QFTs) in various regimes. At criticality the QFTs are minimal models of ${\cal N}=2$ supersymmetric conformal field theory (CFT) - we analyse finite size spectra on open chains with a variety of supersymmetry preserving boundary conditions. Specific staggering perturbations lead to a gapped regime corresponding to massive ${\cal N}=2$ supersymmetric QFT with Chebyshev superpotentials. At `extreme staggering' we uncover a simple physical picture with degenerate supersymmetric vacua and mobile kinks. We connect this kink-picture to the Chebyshev QFTs and use it to derive novel CFT character formulas. For clarity the focus in this paper is on the simplest models, M$_1$, M$_2$ and M$_3$.

Published as SciPost Phys. 3, 004 (2017)

Author comments upon resubmission

In v2 we have incorporated all comments and suggestions by the two referees. Our response to both referees can be found under Replies to the Referee Reports on the SciPost Submission page for version v1 of our manuscript.

List of changes

The main changes are the following.

- In the abstract we added that the focus in this paper is on the simplest models, M_1, M_2 and M_3.
- In the preamble to section 3 we added some remarks on the relation between the boson-parafermion system and the N=2 supersymmetric CFT. We also specified the form of the N=2 supercurrents.
- In section 3.1 we added a remark on the Neveu-Schwarz sectors.
- In section 4.2 we added a sentence clarifying the appearance of additional N=1 supercharges in the M_2 model and hence in the QFTs describing its continuum limit.
- We reconsidered and rearranged the references for the background material in Appendix A, taking into account the recommendations by the second referee.
- Also in the Appendix we added references to the original work on the S-matrices for particles in the supersymmetric sine-Gordon theory.
- Following the remarks by the first referee we made several minor corrections.

Reports on this Submission

Anonymous Report 1 on 2017-6-21 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1703.10079v2, delivered 2017-06-21, doi: 10.21468/SciPost.Report.170






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