Abstract
We present the uplift of the GPPZ solution of the five-dimensional maximal supergravity to ten dimensions. The five dimensional solution involves two real scalar fields, with one of them encoding holographically the (norm of the complex) supersymmetri \( \mathcal{N}=1 \) mass deformation and the other the real part of the gaugino condensate. We embed this solution in a consistent truncation of D = 5 maximal supergravity which involves two complex scalars dual to the complex mass deformations and the complex gaugino condensate, and a U(1) gauge field dual to the U(1)R current, and uplift it to ten dimensions. The ten dimensional solution is completely explicit, with all fields given in terms of elementary functions. The metric and the axion-dilaton agree with those of a partial uplift of the GPPZ flow by Pilch and Warner. We analyze the asymptotics and the singularity structure of the ten dimensional solution. The uplifted solution is singular, but the singularity is milder than that of the five dimensional solution, and there is conformal frame in which the metric is only singular at one point of S5. We compare the asymptotics of the 10d solution with that of the Polchinski-Strassler and Freedman-Minahan solutions, and find agreement with Freedman-Minahan and disagreement with Polchinski-Strassler In particular, we infer that while the Polchinski-Strassler 10d fields satisfy the correct boundary conditions, they do not solve the field equations near the boundary.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena and C. Núñez, Towards the large N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
C. Vafa and E. Witten, A strong coupling test of S duality, Nucl. Phys. B 431 (1994) 3 [hep-th/9408074] [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The supergravity dual of N = 1 super Yang-Mills theory, Nucl. Phys. B 569 (2000) 451 [hep-th/9909047] [INSPIRE].
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged N = 8 D = 5 supergravity, Nucl. Phys. B 259 (1985) 460 [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, Gauged N = 8 supergravity in five-dimensions, Phys. Lett. B 154 (1985) 268 [INSPIRE].
A. Baguet, O. Hohm and H. Samtleben, Consistent type IIB reductions to maximal 5D supergravity, Phys. Rev. D 92 (2015) 065004 [arXiv:1506.01385] [INSPIRE].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D = 10 supergravity on S 5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
O. Aharony, N. Dorey and S.P. Kumar, New modular invariance in the N = 1∗ theory, operator mixings and supergravity singularities, JHEP 06 (2000) 026 [hep-th/0006008] [INSPIRE].
B. Eden, C. Jarczak, E. Sokatchev and Ya. S. Stanev, Operator mixing in N = 4 SYM: the Konishi anomaly revisited, Nucl. Phys. B 722 (2005) 119 [hep-th/0501077] [INSPIRE].
M. Petrini and A. Zaffaroni, The holographic RG flow to conformal and nonconformal theory, hep-th/0002172 [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
D. Elander and M. Piai, Light scalars from a compact fifth dimension, JHEP 01 (2011) 026 [arXiv:1010.1964] [INSPIRE].
O. DeWolfe and D.Z. Freedman, Notes on fluctuations and correlation functions in holographic renormalization group flows, hep-th/0002226 [INSPIRE].
G.W. Gibbons, G.T. Horowitz and P.K. Townsend, Higher dimensional resolution of dilatonic black hole singularities, Class. Quant. Grav. 12 (1995) 297 [hep-th/9410073] [INSPIRE].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Continuous distributions of D3-branes and gauged supergravity, JHEP 07 (2000) 038 [hep-th/9906194] [INSPIRE].
K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys. 4 (2002) 627 [hep-th/0006066] [INSPIRE].
M. Bianchi, O. DeWolfe, D.Z. Freedman and K. Pilch, Anatomy of two holographic renormalization group flows, JHEP 01 (2001) 021 [hep-th/0009156] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [INSPIRE].
J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to N = 4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [INSPIRE].
K.A. Intriligator, Bonus symmetries of N = 4 super Yang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].
M. Günaydin and N. Marcus, The spectrum of the S 5 compactification of the chiral N = 2, D=10 supergravity and the unitary supermultiplets of U(2,2/4), Class. Quant. Grav. 2 (1985) L11 [INSPIRE].
Wolfram Research Inc., Mathematica, version 11.0, U.S.A.
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
K. Skenderis and M. Taylor, Kaluza-Klein holography, JHEP 05 (2006) 057 [hep-th/0603016] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
D.Z. Freedman and J.A. Minahan, Finite temperature effects in the supergravity dual of the N = 1∗ gauge theory, JHEP 01 (2001) 036 [hep-th/0007250] [INSPIRE].
S. Schmidt and K. Skenderis, N = 1 deformations of N = 4 SYM and SUGRA potentials, t appear.
S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, Compact and noncompact gauged supergravity theories in five-dimensions, Nucl. Phys. B 272 (1986) 598 [INSPIRE].
M.J. Duff, G.W. Gibbons and P.K. Townsend, Macroscopic superstrings as interpolating solitons, Phys. Lett. B 332 (1994) 321 [hep-th/9405124] [INSPIRE].
H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
R.M. Wald, General relativity, Chicago Univ. Pr., Chicago U.S.A., (1984) [INSPIRE].
K. Pilch and N.P. Warner, A new supersymmetric compactification of chiral IIB supergravity, Phys. Lett. B 487 (2000) 22 [hep-th/0002192] [INSPIRE].
K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].
A. Brandhuber and K. Sfetsos, An N = 2 gauge theory and its supergravity dual, Phys. Lett. B 488 (2000) 373 [hep-th/0004148] [INSPIRE].
N. Bobev, F.F. Gautason and J. Van Muiden, Precision holography for N = 2∗ on S 4 from type IIB supergravity, JHEP 04 (2018) 148 [arXiv:1802.09539] [INSPIRE].
N. Bobev, F.F. Gautason, B.E. Niehoff and J. van Muiden, Uplifting GPPZ: a ten-dimensional dual of N = 1∗, arXiv:1805.03623 [INSPIRE].
A. Khavaev, K. Pilch and N.P. Warner, New vacua of gauged N = 8 supergravity in five-dimensions, Phys. Lett. B 487 (2000) 14 [hep-th/9812035] [INSPIRE].
H. Nastase and D. Vaman, On the nonlinear KK reductions on spheres of supergravity theories, Nucl. Phys. B 583 (2000) 211 [hep-th/0002028] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, Fortsch. Phys. 65 (2017) 1700048 [arXiv:1401.3360] [INSPIRE].
F. Ciceri, B. de Wit and O. Varela, IIB supergravity and the E 6(6) covariant vector-tensor hierarchy, JHEP 04 (2015) 094 [arXiv:1412.8297] [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: 1805.01919
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
Petrini, M., Samtleben, H., Schmidt, S. et al. The 10d uplift of the GPPZ solution. J. High Energ. Phys. 2018, 26 (2018). https://doi.org/10.1007/JHEP07(2018)026
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2018)026