Abstract
A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer N , an ADE group G, and two nilpotent elements μL,R in G. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for G = SU(k), where AdS7 duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two SU(k) non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS7 vacua, determined by two nilpotent elements, which are naturally interpreted as IIA AdS7 solutions. The BPS equations for domain walls connecting two such vacua can be solved analytically, up to a Nahm equation with certain boundary conditions. The latter admit a solution connecting two vacua if and only if the corresponding nilpotent elements are related by the natural partial ordering, in agreement with the field theory conjecture.
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].
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].
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].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d conformal matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
J.J. Heckman, T. Rudelius and A. Tomasiello, 6d RG flows and nilpotent hierarchies, JHEP 07 (2016) 082 [arXiv:1601.04078] [INSPIRE].
J.J. Heckman, T. Rudelius and A. Tomasiello, Fission, fusion and 6d RG flows, arXiv:1807.10274 [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, JHEP 12 (2014) 003 [arXiv:1404.0711] [INSPIRE].
A. Passias, A. Rota and A. Tomasiello, Universal consistent truncation for 6d/7d gauge/gravity duals, JHEP 10 (2015) 187 [arXiv:1506.05462] [INSPIRE].
E. Malek, H. Samtleben and V. Vall Camell, Supersymmetric AdS 7 and AdS 6 vacua and their minimal consistent truncations from exceptional field theory, Phys. Lett. B 786 (2018) 171 [arXiv:1808.05597] [INSPIRE].
P. Karndumri, RG flows in 6d N = (1, 0) SCFT from SO(4) half-maximal 7D gauged supergravity, JHEP 06 (2014) 101 [arXiv:1404.0183] [INSPIRE].
U.H. Danielsson, G. Dibitetto and S.C. Vargas, A swamp of non-SUSY vacua, JHEP 11 (2017) 152 [arXiv:1708.03293] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
W. Nahm, A simple formalism for the BPS monopole, Phys. Lett. B 90 (1980) 413 [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].
P.B. Kronheimer, Instantons and the geometry of the nilpotent variety, J. Diff. Geom. 32 (1990) 473 [INSPIRE].
N. Bobev, G. Dibitetto, F.F. Gautason and B. Truijen, Holography, brane intersections and six-dimensional SCFTs, JHEP 02 (2017) 116 [arXiv:1612.06324] [INSPIRE].
L. Andrianopoli, R. D’Auria and M. Trigiante, On the dualization of Born-Infeld theories, Phys. Lett. B 744 (2015) 225 [arXiv:1412.6786] [INSPIRE].
A. Hanany and A. Zaffaroni, Tilings, Chern-Simons theories and M2 branes, JHEP 10 (2008) 111 [arXiv:0808.1244] [INSPIRE].
N. Mekareeya, T. Rudelius and A. Tomasiello, T-branes, anomalies and moduli spaces in 6d SCFTs, JHEP 10 (2017) 158 [arXiv:1612.06399] [INSPIRE].
N. Mekareeya, K. Ohmori, H. Shimizu and A. Tomasiello, Small instanton transitions for M5 fractions, JHEP 10 (2017) 055 [arXiv:1707.05785] [INSPIRE].
D.H. Collingwood and W.M. McGovern, Nilpotent orbits in semisimple Lie algebra, Van Nostrand Reinhold, (1993).
F. Apruzzi and M. Fazzi, AdS 7 /CFT 6 with orientifolds, JHEP 01 (2018) 124 [arXiv:1712.03235] [INSPIRE].
I. Bah, A. Passias and A. Tomasiello, AdS 5 compactifications with punctures in massive IIA supergravity, JHEP 11 (2017) 050 [arXiv:1704.07389] [INSPIRE].
E. Bergshoeff, I.G. Koh and E. Sezgin, Yang-Mills/Einstein supergravity in seven-dimensions, Phys. Rev. D 32 (1985) 1353 [INSPIRE].
J. Louis and S. Lüst, Supersymmetric AdS 7 backgrounds in half-maximal supergravity and marginal operators of (1, 0) SCFTs, JHEP 10 (2015) 120 [arXiv:1506.08040] [INSPIRE].
P.K. Townsend and P. van Nieuwenhuizen, Gauged seven-dimensional supergravity, Phys. Lett. B 125 (1983) 41 [INSPIRE].
E. Bergshoeff, D.C. Jong and E. Sezgin, Noncompact gaugings, chiral reduction and dual σ-models in supergravity, Class. Quant. Grav. 23 (2006) 2803 [hep-th/0509203] [INSPIRE].
V.L. Campos, G. Ferretti, H. Larsson, D. Martelli and B.E.W. Nilsson, A study of holographic renormalization group flows in D = 6 and D = 3, JHEP 06 (2000) 023 [hep-th/0003151] [INSPIRE].
F. Apruzzi, G. Dibitetto and L. Tizzano, A new 6d fixed point from holography, JHEP 11 (2016) 126 [arXiv:1603.06576] [INSPIRE].
M. Pernici, K. Pilch, P. van Nieuwenhuizen and N.P. Warner, Noncompact gaugings and critical points of maximal supergravity in seven-dimensions, Nucl. Phys. B 249 (1985) 381 [INSPIRE].
N. Bobev, D. Cassani and H. Triendl, Holographic RG flows for four-dimensional N = 2 SCFTs, JHEP 06 (2018) 086 [arXiv:1804.03276] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Deformations of superconformal theories, JHEP 11 (2016) 135 [arXiv:1602.01217] [INSPIRE].
C. Bachas, J. Hoppe and B. Pioline, Nahm equations, N = 1∗ domain walls and D strings in AdS 5 × S 5, JHEP 07 (2001) 041 [hep-th/0007067] [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: 1810.10013
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
De Luca, G.B., Gnecchi, A., Monaco, G.L. et al. Holographic duals of 6d RG flows. J. High Energ. Phys. 2019, 35 (2019). https://doi.org/10.1007/JHEP03(2019)035
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2019)035