Transverse generalized metrics and 2d sigma models. (English) Zbl 1428.81125
Summary: We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric terms. The resulting notion, a transverse generalized metric, is also what is needed for the dynamics on the reduced phase space of a string theory.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
References:
| [1] | Alekseev, A.; Strobl, T., Current algebras and differential geometry, J. High Energy Phys., 0503, 035 (2005) |
| [2] | Chatzistavrakidis, A.; Deser, A.; Jonke, L.; Strobl, T., Beyond the standard gauging: gauge symmetries of Dirac Sigma Models, J. High Energy Phys., 08, 172 (2016) · Zbl 1390.81313 |
| [3] | Chatzistavrakidis, A.; Deser, A.; Jonke, L.; Strobl, T., Strings in singular space-times and their universal gauge theory, Ann. Henri Poincare, 18, 8, 2641 (2017) · Zbl 1373.81299 |
| [4] | Figueroa-O’Farrill, J. M.; Stanciu, S., Gauged Wess-Zumino terms and equivariant cohomology, Phys. Lett. B, 341, 153 (1994) |
| [5] | Hull, C. M.; Spence, B. J., The gauged nonlinear \(\sigma \)-model with Wess-Zumino term, Phys. Lett. B, 232, 204 (1989) |
| [6] | Kotov, A.; Schaller, P.; Strobl, T., Dirac sigma models, Comm. Math. Phys., 260, 455 (2005) · Zbl 1088.81085 |
| [7] | Kotov, A.; Strobl, T., Generalising geometry—algebroids and sigma models, (Cortes, V., Handbook of Pseudo-Riemannian Geometry and Supersymmetry. Handbook of Pseudo-Riemannian Geometry and Supersymmetry, IRMA Lectures in Mathematics and Theor. Physics, vol. 16 (2010)), chap. 7 · Zbl 1200.53084 |
| [8] | Kotov, A.; Strobl, T., Gauging without initial symmetry, J. Geom. Phys., 99, 184 (2016) · Zbl 1388.70018 |
| [9] | Kotov, A.; Strobl, T., Lie algebroids, gauge theories, and compatible geometrical structures, Rev. Math. Phys., 31, Article 19500156 pp. (2019) · Zbl 1426.53102 |
| [10] | Molino, P., (Riemannian Foliations. Riemannian Foliations, Progress in Mathematics, vol. 73 (1988), Birkhäuser: Birkhäuser Boston) · Zbl 0824.53028 |
| [11] | P. Ševera, Letters to Alan Weinstein about Courant algebroids. See arXiv:1707.00265; P. Ševera, Letters to Alan Weinstein about Courant algebroids. See arXiv:1707.00265 |
| [12] | Ševera, P.; Weinstein, A., Poisson geometry with a 3-form background, Progr. Theoret. Phys. Suppl., 144, 145 (2001) · Zbl 1029.53090 |
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