Abstract
M-theory and string theory predict the existence of many six-dimensional SCFTs. In particular, type IIA brane constructions involving NS5-, D6- and D8-branes conjecturally give rise to a very large class of \( \mathcal{N}=\left(1,0\right) \) CFTs in six dimensions. We point out that these theories sit at the end of RG flows which start from six-dimensional theories which admit an M-theory construction as a M5 stack transverse to \( {\mathrm{\mathbb{R}}}^4/{\mathrm{\mathbb{Z}}}_k\times \mathrm{\mathbb{R}} \). The flows are triggered by Higgs branch expectation values and correspond to D6’s opening up into transverse D8-branes via a Nahm pole. We find a precise correspondence between these CFT’s and the AdS7 vacua found in a recent classification in type II theories. Such vacua involve massive IIA regions, and the internal manifold is topologically S 3. They are characterized by fluxes for the NS three-form and RR two-form, which can be thought of as the near-horizon version of the NS5’s and D6’s in the brane picture; the D8’s, on the other hand, are still present in the AdS7 solution, in the form of an arbitrary number of concentric shells wrapping round S 2’s.
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References
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [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 E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS7 solutions of type-II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [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].
J. Blaback et al., The problematic backreaction of SUSY-breaking branes, JHEP 08 (2011) 105 [arXiv:1105.4879] [INSPIRE].
F.F. Gautason, D. Junghans and M. Zagermann, Cosmological constant, near brane behavior and singularities, JHEP 09 (2013) 123 [arXiv:1301.5647] [INSPIRE].
J. Blaback et al., (Anti-)brane backreaction beyond perturbation theory, JHEP 02 (2012) 025 [arXiv:1111.2605] [INSPIRE].
D. Junghans, D. Schmidt and M. Zagermann, Curvature-induced resolution of anti-brane singularities, JHEP 1410 (2014) 34 [arXiv:1402.6040] [INSPIRE].
B. Janssen, P. Meessen and T. Ortín, The D8-brane tied up: string and brane solutions in massive type IIA supergravity, Phys. Lett. B 453 (1999) 229 [hep-th/9901078] [INSPIRE].
Y. Imamura, 1/4 BPS solutions in massive IIA supergravity, Prog. Theor. Phys. 106 (2001) 653 [hep-th/0105263] [INSPIRE].
D. Youm, Localized intersecting BPS branes, hep-th/9902208 [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].
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].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin systems and the WKB approximation, arXiv:0907.3987 [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
B. Assel, C. Bachas, J. Estes and J. Gomis, Holographic duals of D = 3 N = 4 superconformal field theories, JHEP 08 (2011) 087 [arXiv:1106.4253] [INSPIRE].
O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev. D 84 (2011) 126003 [arXiv:1106.1870] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
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Gaiotto, D., Tomasiello, A. Holography for (1,0) theories in six dimensions. J. High Energ. Phys. 2014, 3 (2014). https://doi.org/10.1007/JHEP12(2014)003
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DOI: https://doi.org/10.1007/JHEP12(2014)003