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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 | |
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| Preprint Link: | https://arxiv.org/abs/1703.10079v2 (pdf) |
| Date submitted: | 2017-06-21 02:00 |
| Submitted by: | Schoutens, Kareljan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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$_3$.
Author comments upon resubmission
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.
Published as SciPost Phys. 3, 004 (2017)