Abstract
We determine the anomaly polynomial of the E-string theory and its higher-rank generalizations, that is, the 6d \( \mathcal{N} \) = (1, 0) superconformal theories on the worldvolume of one or multiple M5-branes embedded within the end-of-the-world brane with E 8 symmetry.
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References
[one] D. Gaiotto, \( \mathcal{N} \) = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
O.J. Ganor and A. Hanany, Small E 8 instantons and tensionless noncritical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120] [INSPIRE].
N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions, Nucl. Phys. B 471 (1996) 121 [hep-th/9603003] [INSPIRE].
E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195 [hep-th/9603150] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds (II), Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
E. Witten, Physical interpretation of certain strong coupling singularities, Mod. Phys. Lett. A 11 (1996) 2649 [hep-th/9609159] [INSPIRE].
Y.-K.E. Cheung, O.J. Ganor and M. Krogh, Correlators of the global symmetry currents of 4D and 6D superconformal theories, Nucl. Phys. B 523 (1998) 171 [hep-th/9710053] [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [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].
D.-E. Diaconescu, G.W. Moore and E. Witten, E 8 gauge theory and a derivation of k-theory from M-theory, Adv. Theor. Math. Phys. 6 (2003) 1031 [hep-th/0005090] [INSPIRE].
E. Diaconescu, G.W. Moore and D.S. Freed, The M-theory three form and E 8 gauge theory, hep-th/0312069 [INSPIRE].
S. Monnier, Global gravitational anomaly cancellation for five-branes, arXiv:1310.2250 [INSPIRE].
E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
A. Bilal and S. Metzger, Anomaly cancellation in M-theory: a critical review, Nucl. Phys. B 675 (2003) 416 [hep-th/0307152] [INSPIRE].
C. Vafa and E. Witten, A one loop test of string duality, Nucl. Phys. B 447 (1995) 261 [hep-th/9505053] [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-branes and M-theory on an orbifold, Nucl. Phys. B 463 (1996) 383 [hep-th/9512219] [INSPIRE].
J.H. Schwarz, Anomaly-free supersymmetric models in six-dimensions, Phys. Lett. B 371 (1996) 223 [hep-th/9512053] [INSPIRE].
M. Berkooz et al., Anomalies, dualities and topology of D = 6 \( \mathcal{N} \) = 1 superstring vacua, Nucl. Phys. B 475 (1996) 115 [hep-th/9605184] [INSPIRE].
V. Sadov, Generalized Green-Schwarz mechanism in F-theory, Phys. Lett. B 388 (1996) 45 [hep-th/9606008] [INSPIRE].
J.J. Heckman, D.R. Morrison and C. Vafa, On the classification of 6D SCFTs and generalized ADE orbifolds, JHEP 05 (2014) 028 [arXiv:1312.5746] [INSPIRE].
O. Aharony and Y. Tachikawa, A holographic computation of the central charges of d = 4, \( \mathcal{N} \) = 2 SCFTs, JHEP 01 (2008) 037 [arXiv:0711.4532] [INSPIRE].
P.S. Aspinwall, Point-like instantons and the Spin(32)/ℤ2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108] [INSPIRE].
P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104] [INSPIRE].
K.A. Intriligator, RG fixed points in six-dimensions via branes at orbifold singularities, Nucl. Phys. B 496 (1997) 177 [hep-th/9702038] [INSPIRE].
J.D. Blum and K.A. Intriligator, Consistency conditions for branes at orbifold singularities, Nucl. Phys. B 506 (1997) 223 [hep-th/9705030] [INSPIRE].
J.D. Blum and K.A. Intriligator, New phases of string theory and 6D RG fixed points via branes at orbifold singularities, Nucl. Phys. B 506 (1997) 199 [hep-th/9705044] [INSPIRE].
I. Brunner and A. Karch, Branes at orbifolds versus Hanany Witten in six-dimensions, JHEP 03 (1998) 003 [hep-th/9712143] [INSPIRE].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, arXiv:1404.0711 [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].
K.A. Intriligator, Anomaly matching and a Hopf-Wess-Zumino term in six-dimensional, \( \mathcal{N} \) = (2,0) field theories, Nucl. Phys. B 581 (2000) 257 [hep-th/0001205] [INSPIRE].
S. Hu and D. Nanopoulos, Hopf-Wess-Zumino term in the effective action of the 6d, (2, 0) field theory revisted, JHEP 10 (2011) 054 [arXiv:1110.0861] [INSPIRE].
R. Bott and A.S. Cattaneo, Integral invariants of {3}-manifolds, J. Differential Geom. 48 (1998) 91 [dg-ga/9710001].
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Ohmori, K., Shimizu, H. & Tachikawa, Y. Anomaly polynomial of E-string theories. J. High Energ. Phys. 2014, 2 (2014). https://doi.org/10.1007/JHEP08(2014)002
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DOI: https://doi.org/10.1007/JHEP08(2014)002