The FZZ duality with boundary

Abstract

The Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality relates Witten's cigar model to sine-Liouville theory. This duality was proven in the path integral formulation and extended to the case of higher genus closed Riemann surfaces by Schomerus and one of the authors. In this note we further extend the duality to the case with boundary. Specifically, we relate D1-branes in the cigar model to D2-branes in the sine-Liouville theory. In particular, the boundary action for D2-branes in the sine-Liouville theory is constructed. We also consider the fermionic version of the FZZ duality. This duality was proven as a mirror symmetry by Hori and Kapustin, but we give an alternative proof in the path integral formulation which directly relates correlation functions. Also here the case with boundary is investigated and the results are consistent with those for branes in N=2 super Liouville field theory obtained by Hosomichi.

41 pages, 2 figures; v2: extended published version

References in corpus (10)

• H^+_3 WZNW model from Liouville field theory
• Branes in the GL(1|1) WZNW-Model
• The GL(1|1)-symplectic fermion correspondence
• Structure constants of the OSP(1|2) WZNW model
• Geometry of branes on supergroups
• Supergroup - extended super Liouville correspondence
• Boundary action of the H3+ model
• From world-sheet supersymmetry to super target spaces
• Topological String on OSP(1|2)/U(1)
• Disk one-point function for non-rational conformal theories

Cited by in corpus (7)

• Supergroup - extended super Liouville correspondence
• Correspondences among CFTs with different W-algebra symmetry
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Correspondences between WZNW models and CFTs with W-algebra symmetry
• Higher rank FZZ-dualities
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras