Abstract
We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.F. Alday, D. Martelli, P. Richmond and J. Sparks, Localization on three-manifolds, JHEP 10 (2013) 095 [arXiv:1307.6848] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The geometry of supersymmetric partition functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].
J. Källén and M. Zabzine, Twisted supersymmetric 5D Yang-Mills theory and contact geometry, JHEP 05 (2012) 125 [arXiv:1202.1956] [INSPIRE].
K. Hosomichi, R.-K. Seong and S. Terashima, Supersymmetric gauge theories on the five-sphere, Nucl. Phys. B 865 (2012) 376 [arXiv:1203.0371] [INSPIRE].
J. Källén, J. Qiu and M. Zabzine, The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere, JHEP 08 (2012) 157 [arXiv:1206.6008] [INSPIRE].
H.-C. Kim and S. Kim, M5-branes from gauge theories on the 5-sphere, JHEP 05 (2013) 144 [arXiv:1206.6339] [INSPIRE].
Y. Imamura, Supersymmetric theories on squashed five-sphere, PTEP 2013 (2013) 013B04 [arXiv:1209.0561] [INSPIRE].
Y. Imamura, Perturbative partition function for squashed S 5, arXiv:1210.6308 [INSPIRE].
J. Qiu and M. Zabzine, 5D super Yang-Mills on Y p,q Sasaki-Einstein manifolds, Commun. Math. Phys. 333 (2015) 861 [arXiv:1307.3149] [INSPIRE].
J. Qiu and M. Zabzine, Factorization of 5D super Yang-Mills theory on Y p,q spaces, Phys. Rev. D 89 (2014) 065040 [arXiv:1312.3475] [INSPIRE].
J. Schmude, Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone, JHEP 01 (2015) 119 [arXiv:1401.3266] [INSPIRE].
Y. Pan, Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry, JHEP 05 (2014) 041 [arXiv:1308.1567] [INSPIRE].
Y. Imamura and H. Matsuno, Supersymmetric backgrounds from 5d N = 1 supergravity, JHEP 07 (2014) 055 [arXiv:1404.0210] [INSPIRE].
Y. Pan, 5D Higgs branch localization, Seiberg-Witten equations and contact geometry, JHEP 01 (2015) 145 [arXiv:1406.5236] [INSPIRE].
L.F. Alday, P.B. Genolini, M. Fluder, P. Richmond and J. Sparks, Supersymmetric gauge theories on five-manifolds, JHEP 08 (2015) 007 [arXiv:1503.09090] [INSPIRE].
Y. Pan and J. Schmude, On rigid supersymmetry and notions of holomorphy in five dimensions, JHEP 11 (2015) 041 [arXiv:1504.00321] [INSPIRE].
A. Pini, D. Rodriguez-Gomez and J. Schmude, Rigid supersymmetry from conformal supergravity in five dimensions, JHEP 09 (2015) 118 [arXiv:1504.04340] [INSPIRE].
L.F. Alday, M. Fluder, P. Richmond and J. Sparks, Gravity dual of supersymmetric gauge theories on a squashed five-sphere, Phys. Rev. Lett. 113 (2014) 141601 [arXiv:1404.1925] [INSPIRE].
L.F. Alday, M. Fluder, C.M. Gregory, P. Richmond and J. Sparks, Supersymmetric gauge theories on squashed five-spheres and their gravity duals, JHEP 09 (2014) 067 [arXiv:1405.7194] [INSPIRE].
L.J. Romans, The F(4) gauged supergravity in six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of M-theory, Class. Quant. Grav. 21 (2004) 4335 [hep-th/0402153] [INSPIRE].
C. Klare, A. Tomasiello and A. Zaffaroni, Supersymmetry on curved spaces and holography, JHEP 08 (2012) 061 [arXiv:1205.1062] [INSPIRE].
C. Klare and A. Zaffaroni, Extended supersymmetry on curved spaces, JHEP 10 (2013) 218 [arXiv:1308.1102] [INSPIRE].
K. Hristov, A. Tomasiello and A. Zaffaroni, Supersymmetry on three-dimensional Lorentzian curved spaces and black hole holography, JHEP 05 (2013) 057 [arXiv:1302.5228] [INSPIRE].
B. Assel, J. Estes and M. Yamazaki, Wilson Loops in 5D N = 1 SCFTs and AdS/CFT, Annales Henri Poincaré 15 (2014) 589 [arXiv:1212.1202] [INSPIRE].
D.L. Jafferis and S.S. Pufu, Exact results for five-dimensional superconformal field theories with gravity duals, JHEP 05 (2014) 032 [arXiv:1207.4359] [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].
J. Qiu, L. Tizzano, J. Winding and M. Zabzine, Gluing Nekrasov partition functions, Commun. Math. Phys. 337 (2015) 785 [arXiv:1403.2945] [INSPIRE].
S. Ferrara, A. Kehagias, H. Partouche and A. Zaffaroni, AdS 6 interpretation of 5D superconformal field theories, Phys. Lett. B 431 (1998) 57 [hep-th/9804006] [INSPIRE].
A. Brandhuber and Y. Oz, The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [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: 1505.04641
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
Alday, L.F., Fluder, M., Gregory, C.M. et al. Supersymmetric solutions to Euclidean Romans supergravity. J. High Energ. Phys. 2016, 100 (2016). https://doi.org/10.1007/JHEP02(2016)100
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)100