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Exact Seiberg-Witten map, induced gravity and topological invariants in non-commutative field theories. (English) Zbl 1160.81469

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.

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
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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
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