Abstract
We develop a superfield approach to compute chiral anomalies in general \( \mathcal{N} \) = (1,0) supersymmetric gauge theories in six dimensions. Within the harmonic-superspace formulation for these gauge theories, the anomalous contributions to the effective action only come from matter and ghost hypermultiplets. By studying the short-distance behaviour of the propagator for the hypermultiplet coupled to a background vector multiplet, we compute the covariant and consistent chiral anomalies. We also provide a superform formulation for the non-abelian anomalous current multiplet in general \( \mathcal{N} \) = (1, 0) supersymmetric gauge theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. 37B (1971) 95 [INSPIRE].
K. Fujikawa, Path integral measure for gauge invariant fermion theories, Phys. Rev. Lett. 42 (1979) 1195 [INSPIRE].
K. Fujikawa, Path integral for gauge theories with fermions, Phys. Rev. D 21 (1980) 2848 [Erratum ibid. D 22 (1980) 1499] [INSPIRE].
R. Stora, Algebraic structure and topological origin of anomalies, in Recent progress in gauge theories, G. ’t Hooft et al. eds., Plenum Press, New York U.S.A. (1984).
B. Zumino, Chiral anomalies and differential geometry, in Relativity, groups and topology II, B.S. De Witt and R. Stora eds., North Holland, Amsterdam The Netherlands (1984).
L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
B. Zumino, Y.-S. Wu and A. Zee, Chiral anomalies, higher dimensions and differential geometry, Nucl. Phys. B 239 (1984) 477 [INSPIRE].
W.A. Bardeen and B. Zumino, Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
H. Leutwyler, Chiral fermion determinants and their anomalies, Phys. Lett. 152B (1985) 78 [INSPIRE].
K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies, Oxford University Press, Oxford U.K. (2004).
F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge University Press, Cambridge U.S.A. (2006).
P.K. Townsend and G. Sierra, Chiral anomalies and constraints on the gauge group in higher dimensional supersymmetric Yang-Mills theories, Nucl. Phys. B 222 (1983) 493 [INSPIRE].
P.H. Frampton and T.W. Kephart, Explicit evaluation of anomalies in higher dimensions, Phys. Rev. Lett. 50 (1983) 1343 [Erratum ibid. 51 (1983) 232] [INSPIRE].
P.H. Frampton and T.W. Kephart, Consistency conditions for Kaluza-Klein axial anomalies, Phys. Rev. Lett. 50 (1983) 1347 [INSPIRE].
P.H. Frampton and T.W. Kephart, The analysis of anomalies in higher space-time dimensions, Phys. Rev. D 28 (1983) 1010 [INSPIRE].
O. Piguet and K. Sibold, The anomaly in the Slavnov identity for N = 1 supersymmetric Yang-Mills theories, Nucl. Phys. B 247 (1984) 484 [INSPIRE].
T.E. Clark and S.T. Love, Supersymmetric effective actions for anomalous internal chiral symmetries, Phys. Lett. B 138 (1984) 289.
N.K. Nielsen, Anomalies of supersymmetric chiral Yang-Mills currents, Nucl. Phys. B 244 (1984) 499 [INSPIRE].
G. Girardi, R. Grimm and R. Stora, Chiral anomalies in N = 1 supersymmetric Yang-Mills theories, Phys. Lett. B 156 (1985) 203.
E. Guadagnini, K. Konishi and M. Mintchev, Non-abelian chiral anomalies in supersymmetric gauge theories, Phys. Lett. B 157 (1985) 37.
K. Konishi and K. Shizuya, Functional integral approach to chiral anomalies in supersymmetric gauge theories, Nuovo Cim. A 90 (1985) 111 [INSPIRE].
L. Bonora, P. Pasti and M. Tonin, ABJ anomalies in supersymmetric Yang-Mills theories, Phys. Lett. B 156 (1985) 341.
L. Bonora, P. Pasti and M. Tonin, The consistent chiral anomaly in supersymmetric Yang-Mills theories, Nucl. Phys. B 261 (1985) 249 [Erratum ibid. B 269 (1986) 745] [INSPIRE].
I.N. McArthur and H. Osborn, Supersymmetric chiral effective action and nonabelian anomalies, Nucl. Phys. B 268 (1986) 573 [INSPIRE].
Y. Ohshima, K. Okuyama, H. Suzuki and H. Yasuta, Remark on the consistent gauge anomaly in supersymmetric theories, Phys. Lett. B 457 (1999) 291 [hep-th/9904096] [INSPIRE].
M. Marinkovic, Wess-Zumino effective action for supersymmetric Yang-Mills theories, Nucl. Phys. B 366 (1991) 74 [INSPIRE].
S.J. Gates, Jr., M.T. Grisaru, M.E. Knutt, S. Penati and H. Suzuki, Supersymmetric gauge anomaly with general homotopic paths, Nucl. Phys. B 596 (2001) 315 [hep-th/0009192] [INSPIRE].
S. Ferrara, J. Wess and B. Zumino, Supergauge multiplets and superfields, Phys. Lett. 51B (1974) 239 [INSPIRE].
P. Breitenlohner and M.F. Sohnius, Superfields, auxiliary fields and tensor calculus for N = 2 extended supergravity, Nucl. Phys. B 165 (1980) 483 [INSPIRE].
S.M. Kuzenko, J. Novak and I.B. Samsonov, The anomalous current multiplet in 6D minimal supersymmetry, JHEP 02 (2016) 132 [arXiv:1511.06582] [INSPIRE].
P.S. Howe and E. Sezgin, Anomaly free tensor Yang-Mills system and its dual formulation, Phys. Lett. B 440 (1998) 50 [hep-th/9806050] [INSPIRE].
P.S. Howe, G. Sierra and P.K. Townsend, Supersymmetry in Six-Dimensions, Nucl. Phys. B 221 (1983) 331 [INSPIRE].
J. Koller, A six-dimensional superspace approach to extended superfields, Nucl. Phys. B 222 (1983) 319 [INSPIRE].
W. Siegel, Superfields in higher dimensional space-time, Phys. Lett. 80B (1979) 220 [INSPIRE].
B.E.W. Nilsson, Superspace action for a six-dimensional nonextended supersymmetric Yang-Mills theory, Nucl. Phys. B 174 (1980) 335 [INSPIRE].
I.L. Buchbinder and N.G. Pletnev, Construction of 6D supersymmetric field models in N = (1,0) harmonic superspace, Nucl. Phys. B 892 (2015) 21 [arXiv:1411.1848] [INSPIRE].
I.L. Buchbinder and N.G. Pletnev, Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background, Phys. Lett. B 744 (2015) 125 [arXiv:1502.03257] [INSPIRE].
I.L. Buchbinder, B.S. Merzlikin and N.G. Pletnev, Induced low-energy effective action in the 6D, \( \mathcal{N} \) = (1, 0) hypermultiplet theory on the vector multiplet background, Phys. Lett. B 759 (2016) 626 [arXiv:1604.06186] [INSPIRE].
I.L. Buchbinder, E.A. Ivanov, B.S. Merzlikin and K.V. Stepanyantz, One-loop divergences in the 6D, \( \mathcal{N} \) = (1, 0) abelian gauge theory, Phys. Lett. B 763 (2016) 375 [arXiv:1609.00975] [INSPIRE].
I.L. Buchbinder, E.A. Ivanov, B.S. Merzlikin and K.V. Stepanyantz, One-loop divergences in 6D, \( \mathcal{N} \) = (1, 0) SYM theory, JHEP 01 (2017) 128 [arXiv:1612.03190] [INSPIRE].
I.L. Buchbinder, E.A. Ivanov, B.S. Merzlikin and K.V. Stepanyantz, Supergraph analysis of the one-loop divergences in 6D, \( \mathcal{N} \) = (1, 0) and \( \mathcal{N} \) = (1, 1) gauge theories, Nucl. Phys. B 921 (2017)127 [arXiv:1704.02530] [INSPIRE].
P.S. Howe, K.S. Stelle and P.C. West, N = 1 D = 6 harmonic superspace, Class. Quant. Grav. 2 (1985) 815 [INSPIRE].
B.M. Zupnik, Six-dimensional supergauge theories in the harmonic superspace, Sov. J. Nucl. Phys. 44 (1986) 512 [Yad. Fiz. 44 (1986) 794] [INSPIRE].
B.M. Zupnik, The action of the supersymmetric N = 2 gauge theory in harmonic superspace, Phys. Lett. B 183 (1987) 175 [INSPIRE].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambrdige U.K. (2001).
L. Mezincescu, On the superfield formulation of O(2) supersymmetry, Dubna preprint JINR-P2-12572 (1979).
I.L. Buchbinder, E.I. Buchbinder, S.M. Kuzenko and B.A. Ovrut, The background field method for N = 2 super Yang-Mills theories in harmonic superspace, Phys. Lett. B 417 (1998) 61 [hep-th/9704214] [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Comments on the background field method in harmonic superspace: nonholomorphic corrections in N = 4 SYM, Mod. Phys. Lett. A 13 (1998) 1623 [hep-th/9804168] [INSPIRE].
S.M. Kuzenko and I.N. McArthur, Effective action of N = 4 super Yang-Mills: N = 2 superspace approach, Phys. Lett. B 506 (2001) 140 [hep-th/0101127] [INSPIRE].
S.M. Kuzenko and I.N. McArthur, Hypermultiplet effective action: N = 2 superspace approach, Phys. Lett. B 513 (2001) 213 [hep-th/0105121] [INSPIRE].
S.M. Kuzenko, Five-dimensional supersymmetric Chern-Simons action as a hypermultiplet quantum correction, Phys. Lett. B 644 (2007) 88 [hep-th/0609078] [INSPIRE].
W.D. Linch, III and G. Tartaglino-Mazzucchelli, Six-dimensional supergravity and projective superfields, JHEP 08 (2012) 075 [arXiv:1204.4195] [INSPIRE].
L. Bonora, P. Pasti and M. Tonin, Chiral anomalies in higher dimensional supersymmetric theories, Nucl. Phys. B 286 (1987) 150 [INSPIRE].
B. de Wit and M.T. Grisaru, Compensating fields and anomalies, in Quantum Field Theory and Quantum Statistics, Volume 2, I.A. Batalin et al. eds.,, Adam Hilger, Bristol, U.K. (1987).
S.M. Kuzenko and W.D. Linch III, On five-dimensional superspaces, JHEP 02 (2006) 038 [hep-th/0507176] [INSPIRE].
A. Galperin, E.A. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic supergraphs. Green functions, Class. Quant. Grav. 2 (1985) 601 [INSPIRE].
E.A. Ivanov, A.V. Smilga and B.M. Zupnik, Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B 726 (2005) 131 [hep-th/0505082] [INSPIRE].
A.V. Smilga, Chiral anomalies in higher-derivative supersymmetric 6D theories, Phys. Lett. B 647 (2007) 298 [hep-th/0606139] [INSPIRE].
A. Davgadorj and R. von Unge, \( \mathcal{N} \) = 2 super Yang-Mills theory in projective superspace, arXiv:1706.07000 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1708.08238
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kuzenko, S.M., Novak, J. & Samsonov, I.B. Chiral anomalies in six dimensions from harmonic superspace. J. High Energ. Phys. 2017, 145 (2017). https://doi.org/10.1007/JHEP11(2017)145
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2017)145