Geometric construction of D-branes in WZW models

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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.
© 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.
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[1] E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [SPIRES]. [2] C.-S. Chu and P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151 [hep-th/9812219] [SPIRES]. [3] V. Schomerus, D-branes and deformation quantization, JHEP 06 (1999) 030 [hep-th/9903205] [SPIRES]. [4] N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep th/9908142] [SPIRES]. [5] C.-S. Chu and P.-M. Ho, Noncommutative D-brane and open string in pp-wave background with B field, Nucl. Phys. B 636 (2002) 141 [hep-th/0203186] [SPIRES]. [6] A.Y. Alekseev, A. Recknagel and V. Schomerus, Non commutative world-volume geometries: branes on SU(2) and fuzzy spheres, JHEP 09 (1999) 023 [hep-th/9908040] [SPIRES]. [7] G. Horcajada and F. Ruiz Ruiz, Quantization of the open string on plane-wave limits of dSn × Sn and non-commutativity outside branes, Nucl. Phys. B 799 (2008) 110 [arXiv:0711.2991] [SPIRES]. [8] J. Rahmfeld and A. Rajaraman, The GS string action on AdS3 × S3 with Ramond-Ramond charge, Phys. Rev. D 60 (1999) 064014 [hep-th/9809164] [SPIRES]. – 20 – JHEP09(2011)020 [9] N. Berkovits, C. Vafa and E. Witten, Conformal field theory of AdS background with Ramond Ramond flux, JHEP 03 (1999) 018 [hep-th/9902098] [SPIRES]. [10] N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach, Superstring theory on AdS2 × S2 as a coset supermanifold, Nucl. Phys. B 567 (2000) 61 [hep-th/9907200] [SPIRES]. [11] A.Y. Alekseev and V. Schomerus, D-branes in the WZW model, Phys. Rev. D 60 (1999) 061901 [hep-th/9812193] [SPIRES]. [12] S. Stanciu, D-branes in an AdS3 background, JHEP 09 (1999) 028 [hep-th/9901122] [SPIRES]. [13] S. Stanciu, D-branes in group manifolds, JHEP 01 (2000) 025 [hep-th/9909163] [SPIRES]. [14] S. Stanciu, A note on D-branes in group manifolds: flux quantization and D0-charge, JHEP 10 (2000) 015 [hep th/0006145] [SPIRES]. [15] J.M. Figueroa-O’Farrill and S. Stanciu, More D-branes in the Nappi-Witten background, JHEP 01 (2000) 024 [hep th/9909164] [SPIRES]. [16] C. Bachas and M. Petropoulos, Anti-de-Sitter D-branes, JHEP 02 (2001) 025 [hep-th/0012234] [SPIRES]. [17] S. Ribault and V. Schomerus, Branes in the 2D black hole, JHEP 02 (2004) 019 [hep th/0310024] [SPIRES]. [18] Y. Hikida, R.R. Nayak and K.L. Panigrahi, D-branes in a big bang/big crunch universe: Nappi Witten gauged WZW model, JHEP 05 (2005) 018 [hep-th/0503148] [SPIRES]. [19] S. Fredenhagen and T. Quella, Generalised permutation branes, JHEP 11 (2005) 004 [hep-th/0509153] [SPIRES]. [20] Y.-K.E. Cheung and L. Freidel, Inner brane: a D3-brane in the Nappi-Witten model from an inner group automorphism, Phys. Rev. D 79 (2009) 126007 [arXiv:0905.0540] [SPIRES]. [21] R. Hern´andez, G. Horcajada and F.R. Ruiz, D-branes with Lorentzian signature in the Nappi-Witten model, JHEP 08 (2011) 047 [arXiv:1104.4730] [SPIRES]. [22] L. Birke, J. Fuchs and C. Schweigert, Symmetry breaking boundary conditions and WZW orbifolds, Adv. Theor. Math. Phys. 3 (1999) 671 [hep-th/9905038] [SPIRES]. [23] J. Fuchs and C. Schweigert, Symmetry breaking boundaries. I: general theory, Nucl. Phys. B 558 (1999) 419 [hep-th/9902132] [SPIRES]. [24] G. Felder, J. Fr¨ohlich, J. Fuchs and C. Schweigert, The geometry of WZW branes, J. Geom. Phys. 34 (2000) 162 [hep-th/9909030] [SPIRES]. [25] V. Schomerus and H. Saleur, The GL(1|1) WZW model: from supergeometry to logarithmic CFT, Nucl. Phys. B 734 (2006) 221 [hep-th/0510032] [SPIRES]. [26] G. G¨otz, T. Quella and V. Schomerus, The WZNW model on PSU(1, 1|2), JHEP 03 (2007) 003 [hep-th/0610070] [SPIRES]. [27] H. Saleur and V. Schomerus, On the SU(2|1) WZNW model and its statistical mechanics applications, Nucl. Phys. B 775 (2007) 312 [hep-th/0611147] [SPIRES]. [28] T. Quella, V. Schomerus and T. Creutzig, Boundary spectra in superspace σ-models, JHEP 10 (2008) 024 [arXiv:0712.3549] [SPIRES]. – 21 – JHEP09(2011)020 [29] T. Creutzig and V. Schomerus, Boundary correlators in supergroup WZNW models, Nucl. Phys. B 807 (2009) 471 [arXiv:0804.3469] [SPIRES]. [30] E. Witten, Nonabelian bosonization in two dimensions, Commun. Math. Phys. 92 (1984) 455 [SPIRES]. [31] C. Klimˇc´ık and P. ˇ Severa, Open strings and D branes in WZNW models, Nucl. Phys. B 488 (1997) 653 [hep th/9609112] [SPIRES]. [32] S. Stanciu and A.A. Tseytlin, D-branes in curved spacetime: Nappi-Witten background, JHEP 06 (1998) 010 [hep th/9805006] [SPIRES]. [33] W.M. Boothby, An introduction to differentiable manifolds and Riemannian geometry, Academic Press, New York U.S.A. (2003). [34] C.R. Nappi and E. Witten, A WZW model based on a nonsemisimple group, Phys. Rev. Lett. 71 (1993) 3751 [hep th/9310112] [SPIRES]. [35] T. Quella and V. Schomerus, Symmetry breaking boundary states and defect lines, JHEP 06 (2002) 028 [hep th/0203161] [SPIRES]. [36] T. Quella, On the hierarchy of symmetry breaking D-branes in group manifolds, JHEP 12 (2002) 009 [hep th/0209157] [SPIRES]. [37] J.M. Maldacena, G.W. Moore and N. Seiberg, Geometrical interpretation of D-branes in gauged WZW models, JHEP 07 (2001) 046 [hep-th/0105038 [SPIRES].