Abstract
We construct a new family of Type IIB backgrounds that are dual to five dimensional conformal field theories compactified and deformed by VEVs of certain operators. This generates an RG flow into a smooth background dual to non-SUSY gapped field theories in four dimensions. We study various holographic observables: a monotonic quantity associated with the number of degrees of freedom, Wilson loops that interpolate between conformal and confining behaviour with the possibility of screening, Entanglement Entropy, etc. We also give a prescription to compute the Holographic Complexity in this type of backgrounds and calculate the spectrum of spin-two glueballs of the field theories.
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J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, Confinement and condensates without fine tuning in supergravity duals of gauge theories, JHEP 05 (1999) 026 [hep-th/9903026] [INSPIRE].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The supergravity dual of N = 1 superYang-Mills theory, Nucl. Phys. B 569 (2000) 451 [hep-th/9909047] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
S.S. Gubser and I.R. Klebanov, Baryons and domain walls in an N = 1 superconformal gauge theory, Phys. Rev. D 58 (1998) 125025 [hep-th/9808075] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N + M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
S.S. Gubser, C.P. Herzog and I.R. Klebanov, Symmetry breaking and axionic strings in the warped deformed conifold, JHEP 09 (2004) 036 [hep-th/0405282] [INSPIRE].
A. Dymarsky, I.R. Klebanov and N. Seiberg, On the moduli space of the cascading SU(M + p) × SU(p) gauge theory, JHEP 01 (2006) 155 [hep-th/0511254] [INSPIRE].
S.S. Gubser, C.P. Herzog and I.R. Klebanov, Variations on the warped deformed conifold, Comptes Rendus Physique 5 (2004) 1031 [hep-th/0409186] [INSPIRE].
J.M. Maldacena and C. Nunez, Towards the large N limit of pure N = 1 superYang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [INSPIRE].
B.S. Acharya, J.P. Gauntlett and N. Kim, Five-branes wrapped on associative three cycles, Phys. Rev. D 63 (2001) 106003 [hep-th/0011190] [INSPIRE].
M. Naka, Various wrapped branes from gauged supergravities, hep-th/0206141 [INSPIRE].
H. Nieder and Y. Oz, Supergravity and D-branes wrapping special Lagrangian cycles, JHEP 03 (2001) 008 [hep-th/0011288] [INSPIRE].
J.P. Gauntlett, N. Kim and D. Waldram, M Five-branes wrapped on supersymmetric cycles, Phys. Rev. D 63 (2001) 126001 [hep-th/0012195] [INSPIRE].
J.D. Edelstein and C. Nunez, D6-branes and M theory geometrical transitions from gauged supergravity, JHEP 04 (2001) 028 [hep-th/0103167] [INSPIRE].
J. Gomis, D-branes, holonomy and M theory, Nucl. Phys. B 606 (2001) 3 [hep-th/0103115] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-Dimensional SCFTs from M5-Branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].
N. Kim and M. Shim, Wrapped Brane Solutions in Romans F (4) Gauged Supergravity, Nucl. Phys. B 951 (2020) 114882 [arXiv:1909.01534] [INSPIRE].
P. Karndumri, Holographic RG flows in six dimensional F (4) gauged supergravity, JHEP 01 (2013) 134 [Erratum ibid. 06 (2015) 165] [arXiv:1210.8064] [INSPIRE].
C. Nunez, I.Y. Park, M. Schvellinger and T.A. Tran, Supergravity duals of gauge theories from F (4) gauged supergravity in six-dimensions, JHEP 04 (2001) 025 [hep-th/0103080] [INSPIRE].
O. Aharony, The NonAdS/nonCFT correspondence, or three different paths to QCD, in the proceedings of the NATO Advanced Study Institute and EC Summer School on Progress in String, Field and Particle Theory, Cargese, France, June 25 – July 11 (2002) [hep-th/0212193] [INSPIRE].
F. Bigazzi, A.L. Cotrone, M. Petrini and A. Zaffaroni, Supergravity duals of supersymmetric four-dimensional gauge theories, Riv. Nuovo Cim. 25N12 (2002) 1 [hep-th/0303191] [INSPIRE].
M. Bertolini, Four lectures on the gauge/gravity correspondence, Int. J. Mod. Phys. A 18 (2003) 5647 [hep-th/0303160] [INSPIRE].
J. Maldacena and D. Martelli, The Unwarped, resolved, deformed conifold: Fivebranes and the baryonic branch of the Klebanov-Strassler theory, JHEP 01 (2010) 104 [arXiv:0906.0591] [INSPIRE].
J. Gaillard, D. Martelli, C. Nunez and I. Papadimitriou, The warped, resolved, deformed conifold gets flavoured, Nucl. Phys. B 843 (2011) 1 [arXiv:1004.4638] [INSPIRE].
E. Caceres, C. Nunez and L.A. Pando-Zayas, Heating up the Baryonic Branch with U-duality: A unified picture of conifold black holes, JHEP 03 (2011) 054 [arXiv:1101.4123] [INSPIRE].
D. Elander, J. Gaillard, C. Nunez and M. Piai, Towards multi-scale dynamics on the baryonic branch of Klebanov-Strassler, JHEP 07 (2011) 056 [arXiv:1104.3963] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Towards a holographic dual of large N(c) QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].
J. Babington et al., Chiral symmetry breaking and pions in nonsupersymmetric gauge/gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals — A Review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [INSPIRE].
R. Casero, C. Nunez and A. Paredes, Towards the string dual of N = 1 SQCD-like theories, Phys. Rev. D 73 (2006) 086005 [hep-th/0602027] [INSPIRE].
R. Casero, C. Nunez and A. Paredes, Elaborations on the String Dual to N = 1 SQCD, Phys. Rev. D 77 (2008) 046003 [arXiv:0709.3421] [INSPIRE].
C. Hoyos-Badajoz, C. Nunez and I. Papadimitriou, Comments on the String dual to N = 1 SQCD, Phys. Rev. D 78 (2008) 086005 [arXiv:0807.3039] [INSPIRE].
F. Benini et al., Unquenched flavors in the Klebanov-Witten model, JHEP 02 (2007) 090 [hep-th/0612118] [INSPIRE].
F. Benini et al., Backreacting flavors in the Klebanov-Strassler background, JHEP 09 (2007) 109 [arXiv:0706.1238] [INSPIRE].
F. Bigazzi et al., D3-D7 Quark-Gluon Plasmas, JHEP 11 (2009) 117 [arXiv:0909.2865] [INSPIRE].
F. Bigazzi, A.L. Cotrone, A. Paredes and A.V. Ramallo, The Klebanov-Strassler model with massive dynamical flavors, JHEP 03 (2009) 153 [arXiv:0812.3399] [INSPIRE].
F. Bigazzi, A.L. Cotrone, A. Paredes and A. Ramallo, Non chiral dynamical flavors and screening on the conifold, Fortsch. Phys. 57 (2009) 514 [arXiv:0810.5220] [INSPIRE].
C. Nunez, A. Paredes and A.V. Ramallo, Unquenched Flavor in the Gauge/Gravity Correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [INSPIRE].
N. Bobev, F.F. Gautason, B.E. Niehoff and J. van Muiden, Uplifting GPPZ: a ten-dimensional dual of \(\mathcal{N}\) = 1∗, JHEP 10 (2018) 058 [arXiv:1805.03623] [INSPIRE].
M. Petrini, H. Samtleben, S. Schmidt and K. Skenderis, The 10d Uplift of the GPPZ Solution, JHEP 07 (2018) 026 [arXiv:1805.01919] [INSPIRE].
J. Armas, G. Batzios and J.P. van der Schaar, Holographic duals of the \(\mathcal{N}\) = 1* gauge theory, JHEP 04 (2023) 021 [arXiv:2212.02777] [INSPIRE].
E. D’Hoker, M. Gutperle, A. Karch and C.F. Uhlemann, Warped AdS6 × S2 in Type IIB supergravity I: Local solutions, JHEP 08 (2016) 046 [arXiv:1606.01254] [INSPIRE].
A. Legramandi and C. Nunez, Electrostatic description of five-dimensional SCFTs, Nucl. Phys. B 974 (2022) 115630 [arXiv:2104.11240] [INSPIRE].
A. Legramandi and C. Nunez, Holographic description of SCFT5 compactifications, JHEP 02 (2022) 010 [arXiv:2109.11554] [INSPIRE].
F. Apruzzi et al., Minkowski4 × S2 solutions of IIB supergravity, Fortsch. Phys. 66 (2018) 1800006 [arXiv:1801.00800] [INSPIRE].
A. Anabalon and S.F. Ross, Supersymmetric solitons and a degeneracy of solutions in AdS/CFT, JHEP 07 (2021) 015 [arXiv:2104.14572] [INSPIRE].
N. Bobev, A.M. Charles and V.S. Min, Euclidean black saddles and AdS4 black holes, JHEP 10 (2020) 073 [arXiv:2006.01148] [INSPIRE].
A. Anabalón, A. Gallerati, S. Ross and M. Trigiante, Supersymmetric solitons in gauged \(\mathcal{N}\) = 8 supergravity, JHEP 02 (2023) 055 [arXiv:2210.06319] [INSPIRE].
C. Nunez, M. Oyarzo and R. Stuardo, Confinement in (1 + 1) dimensions: a holographic perspective from I-branes, JHEP 09 (2023) 201 [arXiv:2307.04783] [INSPIRE].
C. Nunez, M. Oyarzo and R. Stuardo, Confinement and D5 branes, arXiv:2311.17998 [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].
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE].
P. Merrikin, C. Nunez and R. Stuardo, Compactification of 6d N = (1, 0) quivers, 4d SCFTs and their holographic dual Massive IIA backgrounds, Nucl. Phys. B 996 (2023) 116356 [arXiv:2210.02458] [INSPIRE].
E. Witten, Supersymmetric Yang-Mills theory on a four manifold, J. Math. Phys. 35 (1994) 5101 [hep-th/9403195] [INSPIRE].
J.M. Maldacena and C. Nunez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
N. Bobev and P.M. Crichigno, Universal RG Flows Across Dimensions and Holography, JHEP 12 (2017) 065 [arXiv:1708.05052] [INSPIRE].
Y. Bea et al., Compactifications of the Klebanov-Witten CFT and new AdS3 backgrounds, JHEP 05 (2015) 062 [arXiv:1503.07527] [INSPIRE].
N.T. Macpherson et al., Type IIB supergravity solutions with AdS5 from Abelian and non-Abelian T dualities, JHEP 02 (2015) 040 [arXiv:1410.2650] [INSPIRE].
C.F. Uhlemann, Exact results for 5d SCFTs of long quiver type, JHEP 11 (2019) 072 [arXiv:1909.01369] [INSPIRE].
M. Akhond et al., Massive flows in AdS6/CFT5, Phys. Lett. B 840 (2023) 137899 [arXiv:2211.09824] [INSPIRE].
M. Akhond et al., Matrix models and holography: Mass deformations of long quiver theories in 5d and 3d, SciPost Phys. 15 (2023) 086 [arXiv:2211.13240] [INSPIRE].
C. Nunez, L. Santilli and K. Zarembo, Linear Quivers at Large-N, arXiv:2311.00024 [INSPIRE].
A.F. Faedo, C. Nunez and C. Rosen, Consistent truncations of supergravity and \(\frac{1}{2}\)-BPS RG flows in 4d SCFTs, JHEP 03 (2020) 080 [arXiv:1912.13516] [INSPIRE].
A. González Lezcano et al., c-functions in flows across dimensions, JHEP 10 (2022) 083 [arXiv:2207.09360] [INSPIRE].
J. Sonnenschein, What does the string / gauge correspondence teach us about Wilson loops?, in the proceedings of the Advanced School on Supersymmetry in the Theories of Fields, Strings and Branes, Santiago de Compostela, Spain, July 26–31 (1999) [hep-th/0003032] [INSPIRE].
C. Nunez, M. Piai and A. Rago, Wilson Loops in string duals of Walking and Flavored Systems, Phys. Rev. D 81 (2010) 086001 [arXiv:0909.0748] [INSPIRE].
A. Fatemiabhari and C. Nunez, Wilson loops for 5d and 3d conformal linear quivers, Nucl. Phys. B 989 (2023) 116125 [arXiv:2209.07536] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
U. Kol et al., Confinement, Phase Transitions and non-Locality in the Entanglement Entropy, JHEP 06 (2014) 005 [arXiv:1403.2721] [INSPIRE].
N. Jokela and J.G. Subils, Is entanglement a probe of confinement?, JHEP 02 (2021) 147 [arXiv:2010.09392] [INSPIRE].
A. Reynolds and S.F. Ross, Complexity in de Sitter Space, Class. Quant. Grav. 34 (2017) 175013 [arXiv:1706.03788] [INSPIRE].
L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64 (2016) 24 [arXiv:1403.5695] [INSPIRE].
J. Hong, J.T. Liu and D.R. Mayerson, Gauged Six-Dimensional Supergravity from Warped IIB Reductions, JHEP 09 (2018) 140 [arXiv:1808.04301] [INSPIRE].
A.R. Frey, M.P. Grehan and P. Singh, Holographic complexity of the Klebanov-Strassler background, arXiv:2311.18804 [INSPIRE].
J. Yang and A.R. Frey, Complexity, scaling, and a phase transition, JHEP 09 (2023) 029 [arXiv:2307.08229] [INSPIRE].
A. Belin et al., Does Complexity Equal Anything?, Phys. Rev. Lett. 128 (2022) 081602 [arXiv:2111.02429] [INSPIRE].
A. Belin et al., Complexity equals anything II, JHEP 01 (2023) 154 [arXiv:2210.09647] [INSPIRE].
C. Bachas and J. Estes, Spin-2 spectrum of defect theories, JHEP 06 (2011) 005 [arXiv:1103.2800] [INSPIRE].
M. Berg, M. Haack and W. Mueck, Glueballs vs. Gluinoballs: Fluctuation Spectra in Non-AdS/Non-CFT, Nucl. Phys. B 789 (2008) 1 [hep-th/0612224] [INSPIRE].
D.Z. Freedman, C. Nunez, M. Schnabl and K. Skenderis, Fake supergravity and domain wall stability, Phys. Rev. D 69 (2004) 104027 [hep-th/0312055] [INSPIRE].
O. Aharony, E. Schreiber and J. Sonnenschein, Stable nonsupersymmetric supergravity solutions from deformations of the Maldacena-Nunez background, JHEP 04 (2002) 011 [hep-th/0201224] [INSPIRE].
D. Elander, A. Fatemiabhari and M. Piai, Phase transitions and light scalars in bottom-up holography, Phys. Rev. D 108 (2023) 015021 [arXiv:2212.07954] [INSPIRE].
D. Elander, A. Fatemiabhari and M. Piai, Toward minimal composite Higgs models from regular geometries in bottom-up holography, Phys. Rev. D 107 (2023) 115021 [arXiv:2303.00541] [INSPIRE].
A. Fatemiabhari and C. Nunez, From conformal to confining field theories using holography— data release, Zenodo (2024) [https://doi.org/10.5281/zenodo.10546536].
L.J. Romans, The F(4) Gauged Supergravity in Six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
M. Cvetic, H. Lu and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
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].
E. Cáceres, R. Castillo Vásquez, K. Landsteiner and I. Salazar Landea, Holographic a-functions and Boomerang RG flows, JHEP 02 (2024) 019 [arXiv:2310.15983] [INSPIRE].
Acknowledgments
For discussions, comments on the manuscript and for sharing their interesting ideas with us, we wish to thank: Andrés Anabalón, Elena Caceres, Andrew Frey, Yolanda Lozano, Simon Ross, Leonardo Santilli, Jiayue Yang. The work of A.F. is supported by the STFC Consolidated Grant No. ST/V507143/1 and EPSRC Standard Research Studentship (DTP) EP/T517987/1. The work of C. N. is supported by grants ST/X000648/1 and ST/T000813/1.
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Fatemiabhari, A., Nunez, C. From conformal to confining field theories using holography. J. High Energ. Phys. 2024, 160 (2024). https://doi.org/10.1007/JHEP03(2024)160
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DOI: https://doi.org/10.1007/JHEP03(2024)160