Banerjee, Rabin; Yang, Hyun Seok Exact Seiberg-Witten map, induced gravity and topological invariants in non-commutative field theories. (English) Zbl 1160.81469 Nucl. Phys., B 708, No. 1-3, 434-450 (2005). Summary: We revisit the exact Seiberg-Witten (SW) map on Dirac-Born-Infeld actions, making a connection with the deformation quantization scheme. The picture on field dependent induced gravity from non-commutativity becomes more transparent in the context of deformation quantization. We also find an exact SW map for an adjoint scalar field, consistent with that deduced from RR couplings of unstable non-BPS D-branes. The dual description via the exact SW map can again be interpreted as the ordinary field theory coupling to gravity induced by gauge fields. Using the exact SW maps, we further discuss several aspects of topological invariants in non-commutative (NC) gauge theory. Especially, it is shown that the K-theory class on NC instantons is mapped to the usual second Chern class via exact SW map and it leads to an exact SW map between commutative and NC Chern-Simons terms. Cited in 25 Documents MSC: 81T75 Noncommutative geometry methods in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T45 Topological field theories in quantum mechanics PDFBibTeX XMLCite \textit{R. Banerjee} and \textit{H. S. Yang}, Nucl. Phys., B 708, No. 1--3, 434--450 (2005; Zbl 1160.81469) Full Text: DOI arXiv References: [1] Banerjee, R.; Chakraborty, B.; Ghosh, S., Phys. Lett. B, 537, 340 (2002) [2] Szabo, R. J., Phys. Rep., 378, 207 (2003), and references therein [3] Abouelsaood, A.; Callan, C. G.; Nappi, C. R.; Yost, S. A., Nucl. Phys. B, 280, 599 (1987) [4] Seiberg, N.; Witten, E., JHEP, 9909, 032 (1999) [5] Yang, H. S., Exact Seiberg-Witten map and induced gravity from non-commutativity [6] Rivelles, V. O., Phys. Lett. B, 558, 191 (2003) [7] Gross, D. J.; Hashimoto, A.; Itzhaki, N., Adv. Theor. Math. Phys., 4, 893 (2000) [8] Das, S. R.; Rey, S.-J., Nucl. Phys. B, 590, 453 (2000) [9] Kontsevich, M., Deformation quantization of Poisson manifolds I · Zbl 1058.53065 [10] Mukhi, S.; Suryanarayana, N. V., JHEP, 0105, 023 (2001) [11] Grandi, N.; Silva, G. A., Phys. Lett. B, 507, 345 (2001) [12] Andreev, O.; Dorn, H., Phys. Lett. B, 476, 402 (2000) [13] Nakajima, T., Phys. Rev. D, 66, 085008 (2002) [14] Banerjee, R.; Lee, C.; Yang, H. S., Phys. Rev. D, 70, 065015 (2004) [15] Seiberg, N., JHEP, 0009, 003 (2000) [16] Liu, H., Nucl. Phys. B, 614, 305 (2001) [17] Okawa, Y.; Ooguri, H., Phys. Rev. D, 64, 046009 (2001) [18] Liu, H.; Michelson, J., Phys. Lett. B, 518, 134 (2001) [19] Cornalba, L., Adv. Theor. Math. Phys., 4, 271 (2000) [20] Jurčo, B.; Schupp, P.; Wess, J., Nucl. Phys. B, 584, 784 (2000) [21] Abraham, R.; Marsden, J. E., Foundations of Mechanics (1978), Addison-Wesley: Addison-Wesley Reading, MA [22] Bak, D.; Lee, K.; Park, J.-H., Phys. Lett. B, 501, 305 (2001) [23] Jurčo, B.; Schupp, P.; Wess, J., Nucl. Phys. B, 604, 148 (2001) [24] Tian, Y.; Zhu, C.-J.; Song, X.-C., Mod. Phys. Lett. A, 18, 1691 (2003) [25] Das, S. R.; Mukhi, S.; Suryanarayana, N. V., JHEP, 0108, 039 (2001) [26] Banerjee, R., Int. J. Mod. Phys. A, 19, 613 (2004) [27] Kaminsky, K., Nucl. Phys. B, 679, 189 (2004) [28] Polychronakos, A. P., Ann. Phys., 301, 174 (2002) [29] Tseytlin, A. A., Nucl. Phys. B, 501, 41 (1997) [30] Okawa, Y.; Terashima, S., Nucl. Phys. B, 584, 329 (2000) [31] Terashima, S., JHEP, 0002, 007 (2000) [32] Cornalba, L., Adv. Theor. Math. Phys., 4, 1259 (2000) [33] Bak, D.; Lee, K.; Park, J.-H., Phys. Rev. Lett., 87, 0304002 (2001) [34] Martucci, L.; Silva, P. J., Phys. Lett. B, 666, 230 (2003) [35] Nekrasov, N.; Schwarz, A., Commun. Math. Phys., 198, 689 (1998) [36] Douglas, M. R.; Moore, G. W., D-branes, quivers, and ALE instantons This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.