Polymers and percolation in two dimensions and twisted N=2 supersymmetry

Abstract

It is shown how twisted N=2 (k=1) provides for the first time a complete conformal field theory description of the usual geometrical phase transitions in two dimensions, like polymers, percolation or brownian motion. In particular, four point functions of operators with half integer Kac labels are computed, together with geometrical operator products. In addition to Ramond and Neveu Schwartz, a sector with quarter twists has to be introduced. The role of fermions and their various sectors is geometrically interpreted, modular invariant partition functions are built. The presence of twisted N=2 is traced back to the Parisi Sourlas supersymmetry. It is shown that N=2 leads also to new non trivial predictions; for instance the fractal dimension of the percolation backbone in two dimensions is conjectured to be D=25/16, in good agreement with numerical studies.

42 pages (without figures)

References in corpus (1)

• Geometrical Lattice models for N=2 supersymmetric theories in two dimensions

Cited by in corpus (144)

• A Rational Logarithmic Conformal Field Theory
• Symplectic Fermions
• Indecomposable Fusion Products
• A Local Logarithmic Conformal Field Theory
• An algebraic approach to logarithmic conformal field theory
• Logarithmic Minimal Models
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• A crossing probability for critical percolation in two dimensions
• Rare events and breakdown of simple scaling in the Abelian sandpile
• Multicritical Phases of the O(n) Model on a Random Lattice
• Curiosities at c=-2
• Solvable Critical Dense Polymers
• Scaling fields in the two-dimensional abelian sandpile model
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Logarithmic Conformal Field Theories via Logarithmic Deformations
• Virasoro representations and fusion for general augmented minimal models
• The su(2)_{-1/2} WZW model and the beta-gamma system
• On Reducible but Indecomposable Representations of the Virasoro Algebra
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model
• Origin of Logarithmic Operators in Conformal Field Theories
• Holographic applications of logarithmic conformal field theories
• Logarithmic torus amplitudes
• From boundary to bulk in logarithmic CFT
• Logarithmic conformal field theories and AdS correspondence
• Conformal Random Geometry
• Higher Spin Realization of the dS/CFT Correspondence
• Logarithmic Operators and Dynamical Extention of The Symmetry Group in the Bosonic SU(2)_0 and SUSY SU(2)_2 WZNW Models
• The ABC (in any D) of Logarithmic CFT
• Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Singular Vectors in Logarithmic Conformal Field Theories
• Boundary Logarithmic Conformal Field Theory
• The logarithmic triplet theory with boundary
• Continuum limit and symmetries of the periodic gl(1|1) spin chain
• Modular transformation and boundary states in logarithmic conformal field theory
• A modular invariant bulk theory for the c=0 triplet model
• The arboreal gas and the supersphere sigma model
• Copolymer Networks and Stars: Scaling Exponents
• Fusion algebra of critical percolation
• Disordered Dirac Fermions: the Marriage of Three Different Approaches
• Operator Product Expansion in Logarithmic Conformal Field Theory
• A Logarithmic Conformal Field Theory Solution For Two Dimensional Magnetohydrodynamics In Presence of The Alf'ven Effect
• The puzzle of bulk conformal field theories at central charge c=0
• Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories
• Correlation Functions of Dense Polymers and c=-2 Conformal Field Theory
• Relating c<0 and c>0 Conformal Field Theories
• The Sigma Model on Complex Projective Superspaces
• Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
• Exact results at the 2-D percolation point
• On Verlinde-Like Formulas in c_{p,1} Logarithmic Conformal Field Theories
• Boundary States in c=-2 Logarithmic Conformal Field Theory
• Integrable quantum field theories with OSP(m/2n) symmetries
• Conformal field theory correlations in the Abelian sandpile mode
• Ghost Systems: A Vertex Algebra Point of View
• Solvable Critical Dense Polymers on the Cylinder
• PP-waves and logarithmic conformal field theories
• Copolymer Networks: Multifractal dimension spectra in polymer field theory
• Boundary states in boundary logarithmic CFT
• PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
• On $d{S}_4$ extremal surfaces and entanglement entropy in some ghost CFTs
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Pair correlations in sandpile model: a check of logarithmic conformal field theory
• W-Extended Fusion Algebra of Critical Percolation
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
• Geometrical Lattice models for N=2 supersymmetric theories in two dimensions
• Local logarithmic correlators as limits of Coulomb gas integrals
• Modular invariant partition function of critical dense polymers
• The four height variables, boundary correlations, and dissipative defects in the Abelian sandpile model
• Edge Excitations of an Incompressible Fermionic Liquid in a Disorder Magnetic Field
• Dynamical symmetries and causality in non-equilibrium phase transitions
• Critical values of the Yang-Yang functional in the quantum sine-Gordon model
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• New boundary conditions for the c=-2 ghost system
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Logarithmic conformal field theories with continuous weights
• Logarithmic Correlators in Non-relativistic Conformal Field Theory
• Exact logarithmic four-point functions in the critical two-dimensional Ising model
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Reflection Matrices for Integrable $N=1$ Supersymmetric Theories
• Comments on the Quantum Field Theory of the Coulomb Gas Formalism
• Logarithmic bulk and boundary conformal field theory and the full centre construction
• Wind on the boundary for the Abelian sandpile model
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• Logarithmic two-point correlators in the Abelian sandpile model
• Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory
• Ghost Systems Revisited: Modified Virasoro Generators and Logarithmic Conformal Field Theories
• Ghost-spin chains, entanglement and $bc$-ghost CFTs
• On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories
• From world-sheet supersymmetry to super target spaces
• Strong Coupling Fixed Points of Current Interactions and Disordered Fermions in 2D
• Conformal field theory from lattice fermions
• Refined conformal spectra in the dimer model
• Boundary States and Symplectic Fermions
• Logarithmic Conformal Field Theories and Strings in Changing Backgrounds
• Exact Meander Asymptotics: a Numerical Check
• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
• Logarithmic Exotic Conformal Galilean Algebras
• Off-Critical Lattice Analogues of $N=2$ Supersymmetric Quantum Integrable Models
• Extended chiral algebras in the SU(2)_0 WZNW model
• String backgrounds and LCFT
• Two-dimensional spanning webs as (1,2) logarithmic minimal model
• Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations
• Renormalization group for network models of Quantum Hall transitions
• Physical ageing and new representations of some Lie algebras of local scale-invariance
• Lattice Analogues of $N=2$ Superconformal Models via Quantum Group Truncation
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
• Notes on Generalised Nullvectors in logarithmic CFT
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model
• W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
• Oriented Polymers: A Transfer Matrix Calculation
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Three-leg correlations in the two component spanning tree on the upper half-plane
• The Baxter Q Operator of Critical Dense Polymers
• Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
• Representations of ${\bar{U}}_{q}s\ell (2|1)$ at even roots of unity
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups
• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• Integrable N = 2 Landau-Ginzburg Theories from Quotients of Fusion Rings
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Correlation functions of disorder operators in massive ghost theories
• Integrable Floquet systems related to logarithmic conformal field theory
• Critical Behaviour of Spanning Forests on Random Planar Graphs
• The elastic and directed percolation backbone
• Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra
• Infinitely extended Kac table of solvable critical dense polymers
• Yang-Baxter Integrable Dimers on a Strip
• The exact description of NS5-branes in the Penrose limit
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• Non-contractible loops in the dense O(n) loop model on the cylinder
• Conformal Field Theory and Hyperbolic Geometry
• Exponents and bounds for uniform spanning trees in d dimensions
• Some Aspects of c=-2 Theory
• What unitary matrix models are not?
• Analytic Bootstrap for Logarithmic CFT
• Massive ghost theories with a line of defects
• Conformal amplitude hierarchy and the Poincare disk
• Non-trivial fixed point of a ${\psi }_d^4$ fermionic theory, II. Anomalous exponent and scaling operators