Geometric construction of D-branes in WZW models

Abstract

The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=F{J}_{-}$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The equivalence of boundary and gluing conditions of this type is studied in detail. The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over the brane. This approach, when applied to isometries of the form $F=R$ with $R$ a constant Lie algebra automorphism, validates metrically degenerate $R$-twined conjugacy classes as D-branes. It also shows that no D-branes exist in semisimple WZW models for constant\, $F=-R$.

23 pages, discussion of limitations of the gluing condition approach added

References in corpus (6)

• The WZNW model on PSU(1,1|2)
• On the SU(2|1) WZW model and its statistical mechanics applications
• Boundary Spectra in Superspace Sigma-Models
• Boundary Correlators in Supergroup WZNW Models
• Quantization of the open string on plane-wave limits of dS_n x S^n and non-commutativity outside branes
• D-branes with Lorentzian signature in the Nappi-Witten model