Supergroup - extended super Liouville correspondence

Abstract

We derive a relation between correlation functions of supergroup WZNW models and conformal field theories with extended superconformal symmetry. The supergroups considered have a bosonic subgroup of the form SL(2) x A for some Lie group A. The corresponding conformal field theory is a super Liouville field theory coupled with the WZNW model on A. An example is a correspondence between the PSU(1,1|2) WZNW model and small N=4 super Liouville field theory. The OSP(n|2) WZNW model is related to a superconformal field theory with SO(n) extended superconformal symmetry of the Knizhnik-Bershadsky type. In the case n=4 this is simply the large N=(4,4) superconformal symmetry. Besides these two examples we make a general derivation encompassing the WZNW models on supergroups SL(2|n), D(2,1;α), OSP(4|2n), F(4) and G(3) and their relation to models with extended superconformal algebras as symmetry.

30 pages

References in corpus (18)

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• The GL(1|1)-symplectic fermion correspondence
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• Geometry of branes on supergroups
• W-algebras and surface operators in N=2 gauge theories
• Matrix factorisations and D-branes on K3
• Boundary action of the H3+ model
• From world-sheet supersymmetry to super target spaces
• The FZZ duality with boundary
• Topological String on OSP(1|2)/U(1)

Cited by in corpus (14)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• Instanton counting with a surface operator and the chain-saw quiver
• Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Rectangular W-(super)algebras and their representations
• Correspondences among CFTs with different W-algebra symmetry
• The FZZ duality with boundary
• Correspondences between WZNW models and CFTs with W-algebra symmetry
• Higher rank FZZ-dualities
• Gravitational wavefunctions in JT supergravity
• Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins
• Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
• FZZ-triality and large $\mathcal{N}=4$ super Liouville theory
• Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras