Integrable sigma models with theta=pi

Abstract

A fundamental result relevant to spin chains and two-dimensional disordered systems is that the sphere sigma model with instanton coupling theta=pi has a non-trivial low-energy fixed point and a gapless spectrum. This result is extended to two series of sigma models with theta=pi: the SU(N)/SO(N) sigma models flow to the SU(N)_1 WZW theory, while the O(2N)/O(N)\times O(N) models flow to O(2N)_1 (2N free Majorana fermions). These models are integrable, and the exact quasiparticle spectra and S matrices are found. One interesting feature is that charges fractionalize when theta=pi. I compute the energy in a background field, and verify that the perturbative expansions for θ=0 and pi are the same as they must be. I discuss the flows between the two sequences of models, and also argue that the analogous sigma models with Sp(2N) symmetry, the Sp(2N)/U(N) models, flow to Sp(2N)_1.

31 pages, 2 figures. v2: corrects many typos. v3: corrects more typos, adds reference

References in corpus (5)

• The spin quantum Hall effect in unconventional superconductors
• Exact exponents for the spin quantum Hall transition
• Conformal field theory of the integer quantum Hall plateau transition
• Commuting charges and symmetric spaces
• On phase transitions in two-dimensional disordered systems

Cited by in corpus (32)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological delocalization of two-dimensional massless Dirac fermions
• Quantum interference and Aharonov-Bohm oscillations in topological insulators
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Superdiffusion in spin chains
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Superuniversality of superdiffusion
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Quantum integrability and functional equations
• Weak (anti-)localization in doped Z_2-topological insulator
• On the mass spectrum of the two-dimensional O(3) sigma model with theta term
• Continuum limit of fishnet graphs and AdS sigma model
• Integrable quantum field theories with OSP(m/2n) symmetries
• Sigma Models on Flags
• Quantum, higher-spin, local charges in symmetric space sigma models
• The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality
• Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Field theory of non-Hermitian disordered systems
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Quantum integrability of sigma models on AII and CII symmetric spaces
• Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces
• Instantons, renormalons and the theta angle in integrable sigma models
• From S-matrices to the Thermodynamic Bethe Ansatz
• Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
• An Index for Quantum Integrability
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Thermodynamic Bethe ansatz for the AII sigma-models
• On the relationship between sigma models and spin chains
• Notes on index of quantum integrability