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Title: Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit

Abstract

Some time ago, Thies et al. showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase. Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral pair of one-gap periodic Lame potentials with a Darboux displacement depending on the bare mass. We study an unusual supersymmetry of such a second-order Lame system, and show that the associated first-order Bogoliubov-de Gennes Hamiltonian possesses its own nonlinear supersymmetry. The Witten index is ascertained to be zero for both of the related exotic supersymmetric structures, each of which admits several alternatives for the choice of a grading operator. A restoration of the discrete chiral symmetry at zero value of the bare mass, when the kink-antikink crystalline condensate transforms into the kink crystal, is shown to be accompanied by structural changes in both of the supersymmetries. We find that the infinite period limit may or may not change the index. We also explain the origin of the Darboux-dressing phenomenon recently observed in a nonperiodic self-isospectral one-gap Poeschl-Teller system, which describes the Dashen, Hasslacher, and Neveu kink-antikink baryons.

Authors:
 [1];  [1];  [2]
  1. Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile)
  2. Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071, Valladolid (Spain)
Publication Date:
OSTI Identifier:
21537587
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.83.065025; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BARYONS; CHIRAL SYMMETRY; CONDENSATES; HAMILTONIANS; LAGRANGIAN FIELD THEORY; MASS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERIODICITY; POLYMERS; SUPERSYMMETRY; ELEMENTARY PARTICLES; FERMIONS; FIELD THEORIES; HADRONS; MATHEMATICAL OPERATORS; QUANTUM FIELD THEORY; QUANTUM OPERATORS; SYMMETRY; VARIATIONS

Citation Formats

Plyushchay, Mikhail S, Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071, Valladolid, Arancibia, Adrian, and Nieto, Luis-Miguel. Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit. United States: N. p., 2011. Web. doi:10.1103/PHYSREVD.83.065025.
Plyushchay, Mikhail S, Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071, Valladolid, Arancibia, Adrian, & Nieto, Luis-Miguel. Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit. United States. https://doi.org/10.1103/PHYSREVD.83.065025
Plyushchay, Mikhail S, Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071, Valladolid, Arancibia, Adrian, and Nieto, Luis-Miguel. Tue . "Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit". United States. https://doi.org/10.1103/PHYSREVD.83.065025.
@article{osti_21537587,
title = {Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit},
author = {Plyushchay, Mikhail S and Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071, Valladolid and Arancibia, Adrian and Nieto, Luis-Miguel},
abstractNote = {Some time ago, Thies et al. showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase. Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral pair of one-gap periodic Lame potentials with a Darboux displacement depending on the bare mass. We study an unusual supersymmetry of such a second-order Lame system, and show that the associated first-order Bogoliubov-de Gennes Hamiltonian possesses its own nonlinear supersymmetry. The Witten index is ascertained to be zero for both of the related exotic supersymmetric structures, each of which admits several alternatives for the choice of a grading operator. A restoration of the discrete chiral symmetry at zero value of the bare mass, when the kink-antikink crystalline condensate transforms into the kink crystal, is shown to be accompanied by structural changes in both of the supersymmetries. We find that the infinite period limit may or may not change the index. We also explain the origin of the Darboux-dressing phenomenon recently observed in a nonperiodic self-isospectral one-gap Poeschl-Teller system, which describes the Dashen, Hasslacher, and Neveu kink-antikink baryons.},
doi = {10.1103/PHYSREVD.83.065025},
url = {https://www.osti.gov/biblio/21537587}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 83,
place = {United States},
year = {2011},
month = {3}
}