Abstract
We derive the anomaly polynomials of 4d \( \mathcal{N}=2 \) theories that are obtained by wrapping M5-branes on a Riemann surface with arbitrary regular punctures, using anomaly inflow in the corresponding M-theory setup. Our results match the known anomaly polynomials for the 4d \( \mathcal{N}=2 \) class S SCFTs. In our approach, the contributions to the ’t Hooft anomalies due to boundary conditions at the punctures are determined entirely by G4-flux in the 11d geometry. This computation provides a top-down derivation of these contributions that utilizes the geometric definition of the field theories, complementing the previous field-theoretic arguments.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT dual pairs from M 5-branes on Riemann surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-dimensional SCFTs from M 5-branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].
K. Maruyoshi, M. Taki, S. Terashima and F. Yagi, New Seiberg dualities from N = 2 dualities, JHEP 09 (2009) 086 [arXiv:0907.2625] [INSPIRE].
F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].
I. Bah and B. Wecht, New N = 1 superconformal field theories in four dimensions, JHEP 07 (2013) 107 [arXiv:1111.3402] [INSPIRE].
D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
I. Bah, Quarter-BPS AdS 5 solutions in M-theory with a T 2 bundle over a Riemann surface, JHEP 08 (2013) 137 [arXiv:1304.4954] [INSPIRE].
I. Bah, AdS 5 solutions from M 5-branes on Riemann surface and D6-branes sources, JHEP 09 (2015) 163 [arXiv:1501.06072] [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].
D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].
L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
L. Álvarez-Gaumé and P.H. Ginsparg, The structure of gauge and gravitational anomalies, Annals Phys. 161 (1985) 423 [Erratum ibid. 171 (1986) 233] [INSPIRE].
W.A. Bardeen and B. Zumino, Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
I. Bah and E. Nardoni, Structure of anomalies of 4d SCFTs from M 5-branes and anomaly inflow, JHEP 03 (2019) 024 [arXiv:1803.00136] [INSPIRE].
L.F. Alday, F. Benini and Y. Tachikawa, Liouville/Toda central charges from M 5-branes, Phys. Rev. Lett. 105 (2010) 141601 [arXiv:0909.4776] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N = (2, 0) theories, Int. J. Mod. Phys. A 28 (2013) 1340006 [arXiv:1203.2930] [INSPIRE].
Y. Tachikawa, A review of the T N theory and its cousins, PTEP 2015 (2015) 11B102 [arXiv:1504.01481] [INSPIRE].
I. Bah, F. Bonetti, R. Minasian and E. Nardoni, Class S anomalies from M-theory Inflow, Phys. Rev. D 99 (2019) 086020 [arXiv:1812.04016] [INSPIRE].
M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string-string duality: a one loop test, Nucl. Phys. B 452 (1995) 261 [hep-th/9506126] [INSPIRE].
E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234] [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].
J.A. Harvey, R. Minasian and G.W. Moore, Non-Abelian tensor multiplet anomalies, JHEP 09 (1998) 004 [hep-th/9808060] [INSPIRE].
K.A. Intriligator, Anomaly matching and a Hopf-Wess-Zumino term in 6d, N = (2, 0) field theories, Nucl. Phys. B 581 (2000) 257 [hep-th/0001205] [INSPIRE].
P. Yi, Anomaly of (2, 0) theories, Phys. Rev. D 64 (2001) 106006 [hep-th/0106165] [INSPIRE].
E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
R. Bott and A.S. Cattaneo, Integral invariants of 3-manifolds, J. Diff. Geom. 48 (1998) 91 [dg-ga/9710001].
G.W. Gibbons, C.N. Pope and H. Romer, Index theorem boundary terms for gravitational instantons, Nucl. Phys. B 157 (1979) 377 [INSPIRE].
K. Ohmori, H. Shimizu and Y. Tachikawa, Anomaly polynomial of E-string theories, JHEP 08 (2014) 002 [arXiv:1404.3887] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, Anomaly polynomial of general 6d SCFTs, PTEP 2014 (2014) 103B07 [arXiv:1408.5572] [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: 1904.07250
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
Bah, I., Bonetti, F., Minasian, R. et al. Anomaly inflow for M5-branes on punctured Riemann surfaces. J. High Energ. Phys. 2019, 123 (2019). https://doi.org/10.1007/JHEP06(2019)123
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2019)123