2003/02/18 by Hubert Saleur, Birgit Wehefritz–Kaufmann, Birgit Wehefritz-Kaufmann · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Chiral model #Combinatorics #Conformal map #Coset #Geometry #Group (periodic table) #Homogeneous space #Integrable system #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum mechanics #Sigma model #Supergroup #Theoretical physics #Unitary state #Wess–Zumino–Witten model #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(03)00385-7
published as Nucl.Phys. B663 (2003) 443 · 24 pages, 9 figures
arxiv created 2003/02/18 · openalex publication_date 2003/06/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
As a step to understand general patterns of integrability in 1+1 quantum field theories with supergroup symmetry, we study in details the case of OSP(1/2). Our results include the solutions of natural generalizations of models with ordinary group symmetry: the UOSP(1/2)k WZW model with a current current perturbation, the UOSP(1/2) principal chiral model, and the UOSP(1/2)⊗ UOSP(1/2)/UOSP(1/2) coset models perturbed by the adjoint. Graded parafermions are also discussed. A pattern peculiar to supergroups is the emergence of another class of models, whose simplest representative is the OSP(1/2)/OSP(0/2) sigma model, where the (non unitary) orthosymplectic symmetry is realized non linearly (and can be spontaneously broken). For most models, we provide an integrable lattice realization. We show in particular that integrable osp(1/2) spin chains with integer spin flow to UOSP(1/2) WZW models in the continuum limit, hence providing what is to our knowledge the first physical realization of a super WZW model.