Ruiz Ruiz, FernandoHorcajada Reales, Guillermo2023-06-202023-06-202011-091126-670810.1007/JHEP09(2011)020https://hdl.handle.net/20.500.14352/44134© SISSA 2011. The authors are grateful to C.Moreno for conversations, and to MEC and UCM-BSCH, Spain for partial support through grants FPA2008-04906 and 910770-GR35/10-A.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.engjournal articlehttp://dx.doi.org/10.1007/JHEP09(2011)020http://link.springer.comopen access53StringsFísica (Física)22 Física