Abstract
The worldvolume theory of M5-branes on an ADE singularity ℝ 5/Γ G can be Higgsed in various ways, corresponding to the possible nilpotent orbits of G. In the F-theory dual picture, this corresponds to activating T-brane data along two stacks of 7-branes and yields a tensor branch realization for a large class of 6D SCFTs. In this paper, we show that the moduli spaces and anomalies of these T-brane theories are related in a simple, universal way to data of the nilpotent orbits. This often works in surprising ways and gives a nontrivial confirmation of the conjectured properties of T-branes in F-theory. We use this result to formally engineer a class of theories where the IIA picture naïvely breaks down. We also give a proof of the a-theorem for all RG flows within this class of T-brane theories.
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References
E. Witten, Some comments on string dynamics, in the proceedings of Future perspectives in string theory (Strings’95), March 13-18, Los Angeles, U.S.A. (1995), hep-th/9507121 [INSPIRE].
A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].
E. Witten, Five-branes and M-theory on an orbifold, Nucl. Phys. B 463 (1996) 383 [hep-th/9512219] [INSPIRE].
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].
J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Atomic classification of 6D SCFTs, Fortsch. 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].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d conformal matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N}=\left(1,\ 0\right) \) theories on T 2 and class S theories: part I, JHEP 07 (2015) 014 [arXiv:1503.06217] [INSPIRE].
Y. Tachikawa, Frozen singularities in M and F-theory, JHEP 06 (2016) 128 [arXiv:1508.06679] [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, JHEP 12 (2014) 003 [arXiv:1404.0711] [INSPIRE].
D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
J.J. Heckman, T. Rudelius and A. Tomasiello, 6D RG flows and nilpotent hierarchies, JHEP 07 (2016) 082 [arXiv:1601.04078] [INSPIRE].
H. Kraft and C. Procesi, On the geometry of conjugacy classes in classical groups, Comment. Math. Helv. 57 (1982) 539.
S. Cabrera and A. Hanany, Branes and the Kraft-Procesi transition, JHEP 11 (2016) 175 [arXiv:1609.07798] [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS 7 solutions of type-II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [INSPIRE].
F. Apruzzi, M. Fazzi, A. Passias, A. Rota and A. Tomasiello, Six-dimensional superconformal theories and their compactifications from type IIA supergravity, Phys. Rev. Lett. 115 (2015) 061601 [arXiv:1502.06616] [INSPIRE].
S. Cremonesi and A. Tomasiello, 6d holographic anomaly match as a continuum limit, JHEP 05 (2016) 031 [arXiv:1512.02225] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Hall-Littlewood polynomials, JHEP 09 (2014) 178 [arXiv:1403.0585] [INSPIRE].
S. Cecotti, C. Cordova, J.J. Heckman and C. Vafa, T-branes and monodromy, JHEP 07 (2011) 030 [arXiv:1010.5780] [INSPIRE].
K. Kodaira, On compact analytic surfaces, Ann. Math. 77 (1963) 563.
A. Grassi and D.R. Morrison, Anomalies and the Euler characteristic of elliptic Calabi-Yau threefolds, Commun. Num. Theor. Phys. 6 (2012) 51 [arXiv:1109.0042] [INSPIRE].
I. Brunner and A. Karch, Branes and six-dimensional fixed points, Phys. Lett. B 409 (1997) 109 [hep-th/9705022] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
K.A. Intriligator, New string theories in six-dimensions via branes at orbifold singularities, Adv. Theor. Math. Phys. 1 (1998) 271 [hep-th/9708117] [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].
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].
J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Geometry of 6D RG flows, JHEP 09 (2015) 052 [arXiv:1505.00009] [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].
M. Beccaria and A.A. Tseytlin, Conformal anomaly c-coefficients of superconformal 6D theories, JHEP 01 (2016) 001 [arXiv:1510.02685] [INSPIRE].
L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, Generalized F -theorem and the ϵ expansion, JHEP 12 (2015) 155 [arXiv:1507.01960] [INSPIRE].
J.J. Heckman and T. Rudelius, Evidence for C-theorems in 6D SCFTs, JHEP 09 (2015) 218 [arXiv:1506.06753] [INSPIRE].
H. Shimizu and Y. Tachikawa, Anomaly of strings of 6D \( \mathcal{N}=\left(1,\ 0\right) \) theories, JHEP 11 (2016) 165 [arXiv:1608.05894] [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3D Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, T σ ρ (G) theories and their Hilbert series, JHEP 01 (2015) 150 [arXiv:1410.1548] [INSPIRE].
E. Witten, New ‘gauge’ theories in six-dimensions, JHEP 01 (1998) 001 [hep-th/9710065] [INSPIRE].
D.R. Morrison and C. Vafa, F-theory and \( \mathcal{N}=1 \) SCFTs in four dimensions, JHEP 08 (2016) 070 [arXiv:1604.03560] [INSPIRE].
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ArXiv ePrint: 1612.06399
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Mekareeya, N., Rudelius, T. & Tomasiello, A. T-branes, anomalies and moduli spaces in 6D SCFTs. J. High Energ. Phys. 2017, 158 (2017). https://doi.org/10.1007/JHEP10(2017)158
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DOI: https://doi.org/10.1007/JHEP10(2017)158