The GL(1|1)-symplectic fermion correspondence

Abstract

In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1|1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1|1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1|1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition.

34 pages

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Cited by in corpus (29)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• Schur-Weyl Duality for Heisenberg Cosets
• Coset Constructions of Logarithmic (1,p)-Models
• Fusion rules and boundary conditions in the c=0 triplet model
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• Branes in the GL(1|1) WZNW-Model
• Duality of subregular W-algebras and principal W-superalgebras
• The Sigma Model on Complex Projective Superspaces
• Takiff superalgebras and Conformal Field Theory
• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• Tensor structure on the Kazhdan-Lusztig category for affine $\mathfrak{gl}(1|1)$
• Vertex Algebras at the Corner
• Supergroup - extended super Liouville correspondence
• From world-sheet supersymmetry to super target spaces
• W-Algebras Extending Affine gl(1|1)
• Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories
• Branes in the OSP(1|2) WZNW model
• The FZZ duality with boundary
• N=2 Superconformal Symmetry in Super Coset Models
• Continuum Limit of gl(M/N) Spin Chains
• $U_q{\mathfrak{sl}}_2$-invariant non-compact boundary conditions for the XXZ spin chain
• Topological String on OSP(1|2)/U(1)
• A braided monoidal category for free super-bosons
• Yangian Superalgebras in Conformal Field Theory
• Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins
• The Mock Modular Data of a Family of Superalgebras
• Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
• On the gl(1|1) Wess-Zumino-Witten Model
• The free field representation for the $GL(1|1)$ WZW model revisited