SciPost Phys. 3, 004 (2017) ·
published 13 July 2017
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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$_3$.
Prof. Schoutens: "We thank the referee for the c..."
in Report on M$_k$ models: the field theory connection