Symplectic Fermions

Abstract

We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This theory has central charge c=-2 and provides the simplest example of a theory with logarithmic operators. Twisted states with respect to the global SL(2,C)-symmetry of the symplectic fermions are introduced and we describe in detail how one obtains a consistent set of twisted amplitudes. We study orbifold models with respect to finite subgroups of SL(2,C) and obtain their modular invariant partition functions. In the case of the cyclic orbifolds explicit expressions are given for all two-, three- and four-point functions of the fundamental fields. The C_2-orbifold is shown to be isomorphic to the bosonic local logarithmic conformal field theory of the triplet algebra encountered previously. We discuss the relation of the C_4-orbifold to critical dense polymers.

LaTeX2e, 30 pages

References in corpus (9)

• A Local Logarithmic Conformal Field Theory
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• Conformal Algebras of 2D Disordered Systems
• The Haldane-Rezayi Quantum Hall State and Conformal Field Theory
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Singular Vectors in Logarithmic Conformal Field Theories
• Axiomatic Conformal Field Theory
• Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories
• Logarithmic Operators in the Theory of Plateau Transition

Cited by in corpus (151)

• An algebraic approach to logarithmic conformal field theory
• Logarithmic extensions of minimal models: characters and modular transformations
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Associative-algebraic approach to logarithmic conformal field theories
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• Logarithmic Conformal Field Theory: Beyond an Introduction
• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• Fusion rules and logarithmic representations of a WZW model at fractional level
• Solvable Critical Dense Polymers
• Scaling fields in the two-dimensional abelian sandpile model
• Logarithmic Conformal Field Theory: a Lattice Approach
• Logarithmic Conformal Field Theories via Logarithmic Deformations
• Logarithmic intertwining operators and W(2,2p-1)-algebras
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Holographic applications of logarithmic conformal field theories
• Height variables in the Abelian sandpile model: scaling fields and correlations
• From boundary to bulk in logarithmic CFT
• The ABC (in any D) of Logarithmic CFT
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• The logarithmic triplet theory with boundary
• Rényi entropies and negative central charges in non-Hermitian quantum systems
• Continuum limit and symmetries of the periodic gl(1|1) spin chain
• Generalized twisted modules associated to general automorphisms of a vertex operator algebra
• Modular transformation and boundary states in logarithmic conformal field theory
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• sl(2)_{-1/2} and the Triplet Model
• Integrable Boundary Conditions and W-Extended Fusion in the Logarithmic Minimal Models LM(1,p)
• Free fermion resolution of supergroup WZNW models
• Operator Product Expansion in Logarithmic Conformal Field Theory
• Fusion algebra of critical percolation
• A physical approach to the classification of indecomposable Virasoro representations from the blob algebra
• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• The GL(1|1)-symplectic fermion correspondence
• Boundary algebras and Kac modules for logarithmic minimal models
• The Sigma Model on Complex Projective Superspaces
• Boundary height fields in the Abelian sandpile model
• W-Extended Logarithmic Minimal Models
• Boundary States in c=-2 Logarithmic Conformal Field Theory
• On Verlinde-Like Formulas in c_{p,1} Logarithmic Conformal Field Theories
• Operator content of the critical Potts model in d dimensions and logarithmic correlations
• Integrable quantum field theories with OSP(m/2n) symmetries
• The Verlinde formula in logarithmic CFT
• Pre-logarithmic and logarithmic fields in a sandpile model
• Superspace conformal field theory
• Solvable Critical Dense Polymers on the Cylinder
• On the triplet vertex algebra W(p)
• Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• Two-dimensional O(n) models and logarithmic CFTs
• LERW as an example of off-critical SLEs
• Boundary states in boundary logarithmic CFT
• On $d{S}_4$ extremal surfaces and entanglement entropy in some ghost CFTs
• Logarithmic conformal field theory with boundary
• W-Extended Fusion Algebra of Critical Percolation
• Tensor products of psl(2|2) representations
• Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the gl(1|1) periodic spin chain, Howe duality and the interchiral algebra
• Modularization of small quantum groups
• Modularity of logarithmic parafermion vertex algebras
• Geometry of branes on supergroups
• SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• Logarithmic operators and logarithmic conformal field theories
• Local logarithmic correlators as limits of Coulomb gas integrals
• Logarithmic conformal invariance in the Abelian sandpile model
• Painleve equations from Nakajima-Yoshioka blowup relations
• Modular invariant partition function of critical dense polymers
• Notes on non-trivial and logarithmic CFTs with c=0
• Disordered Systems and Logarithmic Conformal Field Theory
• Fermionic Expressions for the Characters of c(p,1) Logarithmic Conformal Field Theories
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum
• 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
• Exact logarithmic four-point functions in the critical two-dimensional Ising model
• Vertex Algebras at the Corner
• On the AdS/CFT Correspondence and Logarithmic Operator
• Integrability and conformal data of the dimer model
• Use of Nilpotent weights in Logarithmic Conformal Field Theories
• SLE local martingales in logarithmic representations
• Galilean contractions of $W$-algebras
• Proposal for a CFT interpretation of Watts' differential equation for percolation
• Minimal Superstrings and Loop Gas Models
• Ghost Systems Revisited: Modified Virasoro Generators and Logarithmic Conformal Field Theories
• Topological M-Strings and Supergroup WZW Models
• Logarithmic two-point correlators in the Abelian sandpile model
• Entanglement Hamiltonian in the non-Hermitian SSH model
• Ghost-spin chains, entanglement and $bc$-ghost CFTs
• On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories
• Logarithmic conformal field theories of type $B_n,\ell =4$ and symplectic fermions
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Polynomial fusion rings of W-extended logarithmic minimal models
• Grothendieck ring and Verlinde-like formula for the W-extended logarithmic minimal model WLM(1,p)
• W-Algebras Extending Affine gl(1|1)
• Boundary States and Symplectic Fermions
• Conformal field theory from lattice fermions
• Kazhdan--Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT
• Extended chiral algebras in the SU(2)_0 WZNW model
• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
• Integrals of Motion for Critical Dense Polymers and Symplectic Fermions
• Twisted chiral de Rham complex, generalized geometry, and T-duality
• A Novel CFT Approach to Bulk Wave Functions in the Fractional Quantum Hall Effect
• Notes on Generalised Nullvectors in logarithmic CFT
• Two-dimensional spanning webs as (1,2) logarithmic minimal model
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• Towards the Construction of Local Logarithmic Conformal Field Theories
• 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)
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge
• Higher-order Galilean contractions
• Edge states and conformal boundary conditions in super spin chains and super sigma models
• $U_q{\mathfrak{sl}}_2$-invariant non-compact boundary conditions for the XXZ spin chain
• A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality
• The Baxter Q Operator of Critical Dense Polymers
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• The second bosonization of the CKP hierarchy
• The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level
• A braided monoidal category for free super-bosons
• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• Correlation functions of disorder operators in massive ghost theories
• Multi-graded Galilean conformal algebras
• Integrable Floquet systems related to logarithmic conformal field theory
• N-level ghost-spins and entanglement
• Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra
• Twisted logarithmic modules of free field algebras
• Two-point boundary correlation functions of dense loop models
• A differential U-module algebra for U=U_q sl(2) at an even root of unity
• Operator Product Expansion and Zero Mode Structure in Logarithmic CFT
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• Infinitely extended Kac table of solvable critical dense polymers
• Yang-Baxter Integrable Dimers on a Strip
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra
• On the gl(1|1) Wess-Zumino-Witten Model
• Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
• Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT
• Logarithmic Vertex Algebras
• SLE($\kappa ,\rho$)and Boundary Coulomb Gas
• A Note on Four-Point Functions in Logarithmic Conformal Field Theory
• Staggered modules of $N=2$ superconformal minimal models
• Some Aspects of c=-2 Theory
• Massive ghost theories with a line of defects
• A non-semisimple non-invertible symmetry
• Commutative algebras in Grothendieck-Verdier categories, rigidity, and vertex operator algebras
• The free field representation for the $GL(1|1)$ WZW model revisited
• Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field
• Free Field realization of the ${\hat{\mathcal{D}}}_q$ Algebra for the $\eta$-$\xi$ system, Integrals of Motion and Characters
• A duality between vertex superalgebras $L_{-3/2}(\mathfrak{osp}(1|2))$ and ${\mathcal{V}}^{(2)}$ and generalizations to logarithmic vertex algebras
• Discrete symplectic fermions on double dimers and their Virasoro representation