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

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.065025· OSTI ID:21537587

Plyushchay, Mikhail S ^[1]; Arancibia, Adrian ^[1]; Nieto, Luis-Miguel ^[2]

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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)

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.

• OSTI ID: 21537587
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevD.83.065025; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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