Abstract
We obtain the anomaly polynomial of strings of general 6d \( \mathcal{N}=\left(1,0\right) \) theories in terms of anomaly inflow. Our computation sheds some light on the reason why the simplest 6d \( \mathcal{N}=\left(1,0\right) \) theory has E 8 flavor symmetry, and also partially explains a curious numerology in F-theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.J. Heckman, D.R. Morrison and C. Vafa, On the classification of 6D SCFTs and generalized ADE orbifolds, JHEP 05 (2014) 028 [Erratum ibid. 06 (2015) 017] [arXiv:1312.5746] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d conformal matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Atomic classification of 6D SCFTs, Fortschr. Phys. 63 (2015) 468 [arXiv:1502.05405] [INSPIRE].
L. Bhardwaj, Classification of 6d \( \mathcal{N}=\left(1,0\right) \) gauge theories, JHEP 11 (2015) 002 [arXiv:1502.06594] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Anomalies, renormalization group flows and the a-theorem in six-dimensional (1, 0) theories, JHEP 10 (2016) 080 [arXiv:1506.03807] [INSPIRE].
J.J. Heckman and T. Rudelius, Evidence for C-theorems in 6D SCFTs, JHEP 09 (2015) 218 [arXiv:1506.06753] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, Anomaly polynomial of general 6D SCFTs, Prog. Theor. Exp. Phys. 2014 (2014) 103B07 [arXiv:1408.5572] [INSPIRE].
K. Intriligator, 6d, \( \mathcal{N}=\left(1,0\right) \) Coulomb branch anomaly matching, JHEP 10 (2014) 162 [arXiv:1408.6745] [INSPIRE].
B. Haghighat, A. Iqbal, C. Kozçaz, G. Lockhart and C. Vafa, M-strings, Commun. Math. Phys. 334 (2015) 779 [arXiv:1305.6322] [INSPIRE].
B. Haghighat, C. Kozçaz, G. Lockhart and C. Vafa, Orbifolds of M-strings, Phys. Rev. D 89 (2014) 046003 [arXiv:1310.1185] [INSPIRE].
B. Haghighat, G. Lockhart and C. Vafa, Fusing E-strings to heterotic strings: E + E → H, Phys. Rev. D 90 (2014) 126012 [arXiv:1406.0850] [INSPIRE].
J. Kim, S. Kim, K. Lee, J. Park and C. Vafa, Elliptic genus of E-strings, arXiv:1411.2324 [INSPIRE].
B. Haghighat, A. Klemm, G. Lockhart and C. Vafa, Strings of minimal 6d SCFTs, Fortschr. Phys. 63 (2015) 294 [arXiv:1412.3152] [INSPIRE].
S. Hohenegger, A. Iqbal and S.-J. Rey, M-strings, monopole strings and modular forms, Phys. Rev. D 92 (2015) 066005 [arXiv:1503.06983] [INSPIRE].
A. Gadde et al., 6d string chains, arXiv:1504.04614 [INSPIRE].
J. Kim, S. Kim and K. Lee, Higgsing towards E-strings, arXiv:1510.03128 [INSPIRE].
B. Haghighat and W. Yan, M-strings in thermodynamic limit: Seiberg-Witten geometry, arXiv:1607.07873 [INSPIRE].
D.R. Morrison and W. Taylor, Classifying bases for 6D F-theory models, Central Eur. J. Phys. 10 (2012) 1072 [arXiv:1201.1943] [INSPIRE].
C. Beem et al., Infinite chiral symmetry in four dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
M. Lemos and P. Liendo, \( \mathcal{N}=2 \) central charge bounds from 2d chiral algebras, JHEP 04 (2016) 004 [arXiv:1511.07449] [INSPIRE].
P. Deligne, La série exceptionnelle de groupes de Lie, C. R. Acad. Sci. Paris 322 (1996) 321.
P. Deligne and R. de Man, La série exceptionnelle de groupes de Lie II, C. R. Acad. Sci. Paris 323 (1996) 577.
A. Grassi and D.R. Morrison, Group representations and the Euler characteristic of elliptically fibered Calabi-Yau threefolds, math.AG/0005196 [INSPIRE].
S.D. Mathur, S. Mukhi and A. Sen, On the classification of rational conformal field theories, Phys. Lett. B 213 (1988) 303 [INSPIRE].
P. Cvitanović, Group theory, Princeton University Press, Princeton U.S.A. (2008) [doi: 10.1515/9781400837670], http://birdtracks.eu/version9.0/index.html.
H.-C. Kim, S. Kim and J. Park, 6d strings from new chiral gauge theories, arXiv:1608.03919 [INSPIRE].
A. Sagnotti, A note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
V. Sadov, Generalized Green-Schwarz mechanism in F-theory, Phys. Lett. B 388 (1996) 45 [hep-th/9606008] [INSPIRE].
D. Freed, J.A. Harvey, R. Minasian and G.W. Moore, Gravitational anomaly cancellation for M-theory five-branes, Adv. Theor. Math. Phys. 2 (1998) 601 [hep-th/9803205] [INSPIRE].
M. Henningson, Self-dual strings in six dimensions: anomalies, the ADE-classification and the world-sheet WZW-model, Commun. Math. Phys. 257 (2005) 291 [hep-th/0405056] [INSPIRE].
D.S. Berman and J.A. Harvey, The self-dual string and anomalies in the M5-brane, JHEP 11 (2004) 015 [hep-th/0408198] [INSPIRE].
M. Henningson and E.P.G. Johansson, Dyonic anomalies, Phys. Lett. B 627 (2005) 203 [hep-th/0508103] [INSPIRE].
H. Kim and P. Yi, D-brane anomaly inflow revisited, JHEP 02 (2012) 012 [arXiv:1201.0762] [INSPIRE].
D. Tong, The holographic dual of AdS 3 × S 3 × S 3 × S 1, JHEP 04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
C. Cordova, T.T. Dumitrescu and X. Yin, Higher derivative terms, toroidal compactification and Weyl anomalies in six-dimensional (2, 0) theories, arXiv:1505.03850 [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: 1608.05894
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Shimizu, H., Tachikawa, Y. Anomaly of strings of 6d \( \mathcal{N}=\left(1,0\right) \) theories. J. High Energ. Phys. 2016, 165 (2016). https://doi.org/10.1007/JHEP11(2016)165
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)165