M$_k$ models: the field theory connection

Fokkema, Thessa; Schoutens, Kareljan

doi:10.21468/SciPostPhys.3.1.004

SciPost Physics

M$_k$ models: the field theory connection

T. Fokkema, K. Schoutens

SciPost Phys. 3, 004 (2017) · published 13 July 2017

doi: 10.21468/SciPostPhys.3.1.004
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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$_3$.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.3.1.004
TI  - M$_k$ models: the field theory connection
PY  - 2017/07/13
UR  - https://scipost.org/SciPostPhys.3.1.004
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 3
IS  - 1
SP  - 004
A1  - Fokkema, Thessa
AU  - Schoutens, Kareljan
AB  - 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$_3$.
ER  -

@Article{10.21468/SciPostPhys.3.1.004,
	title={{M$_k$ models: the field theory connection}},
	author={T. Fokkema and K. Schoutens},
	journal={SciPost Phys.},
	volume={3},
	pages={004},
	year={2017},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.3.1.004},
	url={https://scipost.org/10.21468/SciPostPhys.3.1.004},
}

Cited by 5

Ontology / Topics

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CFT character formulas Chebyshev superpotentials Conformal field theory (CFT) Lattice fermions Mobile kinks N=2 supersymmetric conformal field theory N=2 supersymmetry Quantum field theory (QFT) Supersymmetric vacua

Authors / Affiliation: mappings to Contributors and Organizations

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¹ Thessa Fokkema,
¹ Kareljan Schoutens

¹ Institute of Physics, University of Amsterdam [IoP, UvA]

Funder for the research work leading to this publication

Nederlandse Organisatie voor Wetenschappelijk Onderzoek / Netherlands Organisation for Scientific Research [NWO]