Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case

Abstract

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 $UOSP(1/2)\otimes UOSP(1/2)/UOSP(1/2)$ 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.

arXiv comment24 pages, 9 figures

References in corpus (30)

• Dictionary on Lie Superalgebras
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• On Modular Invariant Partition Functions of Conformal Field Theories with Logarithmic Operators
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• Two-dimensional conformal field theory for disordered systems at criticality
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Conformal field theory of the integer quantum Hall plateau transition
• Lattice regularization of massive and massless integrable field theories
• The exact solution and the finite size behaviour of the $Osp(1|2)$ invariant spin chain
• Disordered Dirac Fermions: the Marriage of Three Different Approaches
• Integrable quantum field theories with OSP(m/2n) symmetries
• Exact S-matrices for supersymmetric sigma models and the Potts model
• Graded Parafermions
• Integrable perturbations of CFT with complex parameter: the $M_{3/5}$ model and its generalizations
• On the Supersymplectic Homogeneous Superspace Underlying the OSp(1/2) Coherent States
• A Free Field Representation of the Osp(2|2) current algebra at level k=-2, and Dirac Fermions in a random SU(2) gauge potential
• Modules Over Affine Lie Superalgebras
• Bethe ansatz solution of the $Osp(1|2n)$ invariant spin chain
• A local and integrable lattice regularization of the massive Thirring model
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Fusion rules and singular vectors of the osp(1|2) current algebra
• On the free field realization of the osp(1|2) current algebra
• Structure constants for the osp(1|2) current algebra
• Thermodynamic Bethe ansatz equation from fusion hierarchy of osp(1|2) integrable spin chain
• Renormalization group for network models of Quantum Hall transitions
• Thermodynamics of osp(1|2) Integrable Spin Chain: Finite Size Correction
• osp(1|2) Conformal Field Theory

Cited by in corpus (20)

• Fermionic field theory for trees and forests
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Structure constants of the OSP(1|2) WZNW model
• The continuum limit of $a_{N-1}^{(2)}$ spin chains
• Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• Dual description of $\eta$-deformed OSP sigma models
• Solutions to the Yang-Baxter equations with $os{p}_q(1|2)$ symmetry: Lax operators
• Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]
• Quantum Spheres for OSp_q(1/2)
• Covariant Differential Calculi on $S{P}_q^{1|2}$
• Fusion Rules of the Lowest Weight Representations of osp_q(1|2) at Roots of Unity: Polynomial Realization and Degeneration at Roots of Unity
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups
• Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials
• Completing the solution for the $OSp(1|2)$ spin chain
• Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]
• On currents in the $O(n)$ loop model
• Deconfined quantum criticality with internal supersymmetry