%0 Journal Article
%A Ruiz Ruiz, Fernando
%A Horcajada Reales, Guillermo
%T Geometric construction of D-branes in WZW models
%D 2011
%@ 1126-6708
%U https://hdl.handle.net/20.500.14352/44134
%X The geometric description of D-branes inWZWmodels is pushed forward. Our starting point is a gluing condition J+ = FJ− 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.
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