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Noncommutativity relations in type IIB theory and their supersymmetry. (English) Zbl 1291.81368

Summary: In the present paper we investigate noncommutativity of \(D\)9 and \(D\)5-brane world-volumes embedded in space-time of type IIB superstring theory. Boundary conditions, which preserve half of the initial supersymmetry, are treated as canonical constraints. Solving the constraints we obtain original coordinates in terms of the effective coordinates and momenta. Presence of momenta induces noncommutativity of string endpoints. We show that noncommutativity relations are connected by \(N = 1\) supersymmetry transformations and noncommutativity parameters are components of \(N = 1\) supermultiplet.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
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References:

[1] J. Polchinski, String theory. Volume II, Cambridge University Press, Cambridge U.K. (1998). · Zbl 1006.81521 · doi:10.1017/CBO9780511618123
[2] K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory - A modern introduction, Cambridge University Press, Cambridge U.K. (2007). · Zbl 1123.81001
[3] N. Berkovits and P.S. Howe, Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys.B 635 (2002) 75 [hep-th/0112160] [SPIRES]. · Zbl 0996.81075 · doi:10.1016/S0550-3213(02)00352-8
[4] P.A. Grassi, G. Policastro and P. van Nieuwenhuizen, The massless spectrum of covariant superstrings, JHEP11 (2002) 004 [hep-th/0202123] [SPIRES]. · doi:10.1088/1126-6708/2002/11/004
[5] P.A. Grassi, G. Policastro and P. van Nieuwenhuizen, On the BRST cohomology of superstrings with/without pure spinors, Adv. Theor. Math. Phys.7 (2003) 499 [hep-th/0206216] [SPIRES]. · Zbl 1053.81039
[6] P.A. Grassi, G. Policastro and P. van Nieuwenhuizen, The covariant quantum superstring and superparticle from their classical actions, Phys. Lett.B 553 (2003) 96 [hep-th/0209026] [SPIRES]. · Zbl 1006.81072
[7] M.J. Duff, R.R. Khuri and J.X. Lu, String solitons, Phys. Rept.259 (1995) 213 [hep-th/9412184] [SPIRES]. · doi:10.1016/0370-1573(95)00002-X
[8] E. Kiritsis, Introduction to superstring theory, hep-th/9709062 [SPIRES]. · Zbl 0911.53049
[9] F. Ardalan, H. Arfaei and M.M. Sheikh-Jabbari, Dirac quantization of open strings and noncommutativity in branes, Nucl. Phys.B 576 (2000) 578 [hep-th/9906161] [SPIRES]. · Zbl 1056.81539 · doi:10.1016/S0550-3213(00)00096-1
[10] C.-S. Chu and P.-M. Ho, Constrained quantization of open string in background B field and noncommutative D-brane, Nucl. Phys.B 568 (2000) 447 [hep-th/9906192] [SPIRES]. · Zbl 0951.81093 · doi:10.1016/S0550-3213(99)00685-9
[11] T. Lee, Canonical quantization of open string and noncommutative geometry, Phys. Rev.D 62 (2000) 024022 [hep-th/9911140] [SPIRES].
[12] B. Sazdovic, Dilaton field induces commutative Dp-brane coordinate, Eur. Phys. J.C 44 (2005) 599 [hep-th/0408131] [SPIRES]. · Zbl 1191.81177 · doi:10.1140/epjc/s2005-02385-7
[13] B. Nikolic and B. Sazdovic, Gauge symmetries decrease the number of Dp-brane dimensions, Phys. Rev.D 74 (2006) 045024 [hep-th/0604129] [SPIRES].
[14] B. Nikolic and B. Sazdovic, Gauge symmetries decrease the number of Dp-brane dimensions. II. Inclusion of the Liouville term, Phys. Rev.D 75 (2007) 085011 [hep-th/0611191] [SPIRES].
[15] B. Nikolic and B. Sazdovic, Noncommutativity in space-time extended by Liouville field, Adv. Theor. Math. Phys.14 (2010) 1 [arXiv:0711.4463] [SPIRES]. · Zbl 1201.81102
[16] B. Nikolic and B. Sazdovic, Type I background fields in terms of type IIB ones, Phys. Lett.B 666 (2008) 400 [arXiv:0804.2617] [SPIRES]. · Zbl 1328.81184
[17] B. Nikolic and B. Sazdovic, D5-brane type-I superstring background fields in terms of type IIB ones by canonical method and T-duality approach, Nucl. Phys.B 836 (2010) 100 [arXiv:1004.1962] [SPIRES]. · Zbl 1206.81108 · doi:10.1016/j.nuclphysb.2010.04.013
[18] N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP09 (1999) 032 [hep-th/9908142] [SPIRES]. · doi:10.1088/1126-6708/1999/09/032
[19] J. de Boer, P.A. Grassi and P. van Nieuwenhuizen, Non-commutative superspace from string theory, Phys. Lett.B 574 (2003) 98 [hep-th/0302078] [SPIRES]. · Zbl 1058.81076
[20] M. Dimitrijević, V. Radovanović and J. Wess, Field Theory on Nonanticommutative Superspace, JHEP12 (2007) 059 [arXiv:0710.1746] [SPIRES]. · Zbl 1246.81397 · doi:10.1088/1126-6708/2007/12/059
[21] F. Riccioni, Truncations of the D9-brane action and type-I strings, Phys. Lett.B 560 (2003) 223 [hep-th/0301021] [SPIRES]. · Zbl 1094.81546
[22] N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059 [SPIRES]. · Zbl 1069.81570
[23] P.A. Grassi, G. Policastro, M. Porrati and P. Van Nieuwenhuizen, Covariant quantization of superstrings without pure spinor constraints, JHEP10 (2002) 054 [hep-th/0112162] [SPIRES]. · doi:10.1088/1126-6708/2002/10/054
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