Geometry of branes on supergroups

Abstract

In this note we analyze the geometry of maximally symmetric boundary conditions in Lie supergroup Wess-Zumino-Novikov-Witten models. We find that generically the worldvolume of a brane is a twisted superconjugacy class, very much like in the Lie group case. Whenever the brane is not completely delocalized in the fermionic directions a new atypical class of branes arises. We give an example of these new branes and show for type I supergroups and trivial gluing conditions that they can be naturally associated with atypical representations of the affine Lie superalgebra.

25 pages, 1 figure

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Cited by in corpus (20)

• Fusion rules and boundary conditions in the c=0 triplet model
• Integrability of Green-Schwarz Sigma Models with Boundaries
• Branes in the GL(1|1) WZNW-Model
• Boundary Spectra in Superspace Sigma-Models
• The GL(1|1)-symplectic fermion correspondence
• Superspace conformal field theory
• Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions
• Supergroup - extended super Liouville correspondence
• From world-sheet supersymmetry to super target spaces
• Branes in the OSP(1|2) WZNW model
• The FZZ duality with boundary
• Yangian in the Twistor String
• N=2 Superconformal Symmetry in Super Coset Models
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Edge states and conformal boundary conditions in super spin chains and super sigma models
• Yangian Superalgebras in Conformal Field Theory
• Disk one-point function for non-rational conformal theories
• 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