Anomaly freedom in Seiberg-Witten noncommutative gauge theories

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Google Scholar
Research Projects
Organizational Units
Journal Issue
We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the epsilon(mu1mu2mu3mu4) part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter theta(munu). And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.
© SISSA/ISAS 2003. CPM and FRR are grateful to CICyT, Spain for partial support through grant No. BFM2002-00950.
Unesco subjects
[1] J. Madore, S. Schraml, P. Schupp and J. Wess, Gauge theory on noncommutative spaces, Eur. Phys. J. C 16 (2000) 161 [hep-th/0001203]. [2] B. Jurco, S. Schraml, P. Schupp and J. Wess, Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces, Eur. Phys. J. C 17 (2000) 521 [hep-th/0006246]. [3] N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032 [hep-th/9908142]. [4] B. Jurco, P. Schupp and J. Wess, Nonabelian noncommutative gauge theory via noncommutative extra dimensions, Nucl. Phys. B 604 (2001) 148 [hep-th/0102129]. [5] B. Jurco, L. Moller, S. Schraml, P. Schupp and J. Wess, Construction of non-abelian gauge theories on noncommutative spaces, Eur. Phys. J. C 21 (2001) 383 [hep th/0104153]. [6] X. Calmet, B. Jurco, P. Schupp, J. Wess and M. Wohlgenannt, The standard model on non-commutative space time, Eur. Phys. J. C 23 (2002) 363 [hep-ph/0111115]. [7] S.M. Carroll, J.A. Harvey, V.A. Kostelecky, C.D. Lane and T. Okamoto, Noncommutative ¯eld theory and Lorentz violation, Phys. Rev. Lett. 87 (2001) 141601 [hep th/0105082]. [8] C.E. Carlson, C.D. Carone and R.F. Lebed, Bounding noncommutative QCD, Phys. Lett. B 518 (2001) 201 [hep ph/0107291]. [9] W. Behr et al., The z! °°; gg decays in the noncommutative standard model, hep-ph/0202121. [10] C.E. Carlson, C.D. Carone and R.F. Lebed, Supersymmetric noncommutative QED and Lorentz violation, Phys. Lett. B 549 (2002) 337 [hep-ph/0209077]. [11] P. Schupp, J. Trampetic, J. Wess and G. Ra®elt, The photon neutrino interaction in non-commutative gauge ¯eld theory and astrophysical bounds, hep-ph/0212292. [12] P. Minkowski, P. Schupp and J. Trampetic, Non commutative `*-charge radius' and `*-dipole moment' of the neutrino, hep-th/0302175. [13] P. Aschieri, B. Jurco, P. Schupp and J. Wess, Non commutative GUTs, standard model and C, P, T, Nucl. Phys. B 651 (2003) 45 [hep-th/0205214]. [14] G. Barnich and M. Henneaux, Renormalization of gauge invariant operators and anomalies in Yang-Mills theory, Phys. Rev. Lett. 72 (1994) 1588 [hep-th/9312206]. [15] G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in the anti¯eld formalism, 2. Application to Yang-Mills theory, Commun. Math. Phys. 174 (1995) 93 [hep th/9405194]. [16] G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in gauge theories, Phys. Rept. 338 (2000) 439 [hep-th/0002245]. { 24 { JHEP07(2003)068 [17] R. Wulkenhaar, Non-renormalizability of theta-expanded noncommutative QED, J. High Energy Phys. 03 (2002) 024 [hep th/0112248]. [18] C.P. Martin, The gauge anomaly and the Seiberg-Witten map, Nucl. Phys. B 652 (2003) 72 [hep th/0211164]. [19] R. Banerjee and S. Ghosh, Seiberg-Witten map and the axial anomaly in noncommutative ¯eld theory, Phys. Lett. B 533 (2002) 162 [hep-th/0110177]. [20] R. Banerjee, Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings, hep-th/0301174. [21] B.L. Cerchiai, A.F. Pasqua and B. Zumino, The Seiberg Witten map for noncommutative gauge theories, hep th/0206231. [22] P. Breitenlohner and D. Maison, Dimensional renormalization and the action principle, Commun. Math. Phys. 52 (1977) 11. [23] G. Barnich, F. Brandt and M. Grigoriev, Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups, J. High Energy Phys. 08 (2002) 023 [hep th/0206003]. [24] H. Georgi and S.L. Glashow, Gauge theories without anomalies, Phys. Rev. D 6 (1972) 429. [25] J.M. Gracia-Bondia and C.P. Martin, Chiral gauge anomalies on noncommutative R4, Phys. Lett. B 479 (2000) 321 [hep-th/0002171]. [26] L. Bonora, M. Schnabl and A. Tomasiello, A note on consistent anomalies in noncommutative YM theories, Phys. Lett. B 485 (2000) 311 [hep-th/0002210]. [27] D.J. Gross and R. Jackiw, E®ect of anomalies on quasirenormalizable theories, Phys. Rev. D 6 (1972) 477. [28] F. Brandt, N. Dragon and M. Kreuzer, Completeness and nontriviality of the solutions of the consistency conditions, Nucl. Phys. B 332 (1990) 224.