Abstract
M5-branes on an ADE singularity are described by certain six-dimensional “conformal matter” superconformal field theories. Their Higgs moduli spaces contain information about various dynamical processes for the M5s; however, they are not directly accessible due to the lack of a Lagrangian formulation. Using anomaly matching, we compute their dimensions. The result implies that M5 fractions can recombine in several different ways, where the M5s are leaving behind frozen versions of the singularity. The anomaly polynomial gives hints about the nature of the freezing. We also check the Higgs dimension formula by comparing it with various existing conjectures for the CFTs one obtains by torus compactifications down to four and three dimensions. Aided by our results, we also extend those conjectures to compactifications of theories not previously considered. These involve class \( \mathcal{S} \) theories with twisted punctures in four dimensions, and affine-Dynkin-shaped quivers in three dimensions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K.A. Intriligator, RG fixed points in six-dimensions via branes at orbifold singularities, Nucl. Phys. B 496 (1997) 177 [hep-th/9702038] [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].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
N.J. Evans, C.V. Johnson and A.D. Shapere, Orientifolds, branes and duality of 4 − D gauge theories, Nucl. Phys. B 505 (1997) 251 [hep-th/9703210] [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, JHEP 12 (2014) 003 [arXiv:1404.0711] [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. Cecotti, C. Cordova, J.J. Heckman and C. Vafa, T-Branes and Monodromy, JHEP 07 (2011) 030 [arXiv:1010.5780] [INSPIRE].
J.J. Heckman, T. Rudelius and A. Tomasiello, 6D RG Flows and Nilpotent Hierarchies, JHEP 07 (2016) 082 [arXiv:1601.04078] [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].
N. Mekareeya, T. Rudelius and A. Tomasiello, T-branes, Anomalies and Moduli Spaces in 6D SCFTs, arXiv:1612.06399 [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].
E. Witten, Toroidal compactification without vector structure, JHEP 02 (1998) 006 [hep-th/9712028] [INSPIRE].
J. de Boer et al., Triples, fluxes and strings, Adv. Theor. Math. Phys. 4 (2002) 995 [hep-th/0103170] [INSPIRE].
Y. Tachikawa, Frozen singularities in M and F-theory, JHEP 06 (2016) 128 [arXiv:1508.06679] [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. 1506 (2015) 017] [arXiv:1312.5746] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N}=\left(1,0\right) \) theories on S 1 /T 2 and class S theories: part II, JHEP 12 (2015) 131 [arXiv:1508.00915] [INSPIRE].
K. Ohmori, Six-Dimensional Superconformal Field Theories and Their Torus Compactifications, Ph.D. Thesis, University of Tokyo, Tokyo Japan (2016), http://www2.yukawa.kyoto-u.ac.jp/~soken.editorial/shuron/ohmori_k16.pdf.
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].
I. Bena, J. Blåbäck, R. Minasian and R. Savelli, There and back again: A T-brane’s tale, JHEP 11 (2016) 179 [arXiv:1608.01221] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, Anomaly polynomial of general 6d SCFTs, PTEP 2014 (2014) 103B07 [arXiv:1408.5572] [INSPIRE].
A. Hanany and N. Mekareeya, Tri-vertices and SU(2)’s, JHEP 02 (2011) 069 [arXiv:1012.2119] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto duality for the twisted A 2N − 1 series, JHEP 05 (2015) 075 [arXiv:1212.3952] [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, Coulomb branch Hilbert series and Three Dimensional Sicilian Theories, JHEP 09 (2014) 185 [arXiv:1403.2384] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the Z3-twisted D4 Theory, arXiv:1601.02077 [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the Twisted E 6 Theory, JHEP 04 (2015) 173 [arXiv:1501.00357] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the Twisted D-Series, arXiv:1309.2299 [INSPIRE].
O. Chacaltana, J. Distler, A. Trimm and Y. Zhu, Tinkertoys for the E7 Theory, arXiv:1704.07890 [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Coulomb Branch and The Moduli Space of Instantons, JHEP 12 (2014) 103 [arXiv:1408.6835] [INSPIRE].
M. Del Zotto, C. Vafa and D. Xie, Geometric engineering, mirror symmetry and \( 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} \), JHEP 11 (2015) 123 [arXiv:1504.08348] [INSPIRE].
Y. Tachikawa, \( \mathcal{N}=2 \) supersymmetric dynamics for pedestrians, Lect. Notes Phys. 890 (2014) 1 [arXiv:1312.2684] [INSPIRE].
M. Porrati and A. Zaffaroni, M theory origin of mirror symmetry in three-dimensional gauge theories, Nucl. Phys. B 490 (1997) 107 [hep-th/9611201] [INSPIRE].
D. Gaiotto and E. Witten, S-duality of Boundary Conditions In N = 4 Super Yang-Mills Theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [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].
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: 1707.05785
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
Mekareeya, N., Ohmori, K., Shimizu, H. et al. Small instanton transitions for M5 fractions. J. High Energ. Phys. 2017, 55 (2017). https://doi.org/10.1007/JHEP10(2017)055
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)055