Abstract
In this article we report on a preliminary study, via Holography, of infrared fixed points in a putative strongly coupled SU(N c ) gauge theory, with N f fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently effective or a bottom up approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: \( {\mathrm{AdS}}_m\times {\mathrm{\mathbb{R}}}^n \)-type, which has appeared in the literature before; and AdS m ×EAdS n -type, where m and n are suitable integers. Both these classes of solutions are non-perturbative in back-reaction. The AdS m ×EAdS n -type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS5 ultraviolet to both an AdS2 and an AdS3 IR.
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References
W.E. Caswell, Asymptotic Behavior of Nonabelian Gauge Theories to Two Loop Order, Phys. Rev. Lett. 33 (1974) 244 [INSPIRE].
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions, Nucl. Phys. B 196 (1982) 189 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].
A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: Some exact results, JHEP 11 (2007) 074 [arXiv:0709.0570] [INSPIRE].
M.G. Alford, A. Schmitt, K. Rajagopal and T. Schäfer, Color superconductivity in dense quark matter, Rev. Mod. Phys. 80 (2008) 1455 [arXiv:0709.4635] [INSPIRE].
A.F. Faedo, A. Kundu, D. Mateos and J. Tarrío, (Super) Yang-Mills at Finite Heavy-Quark Density, JHEP 02 (2015) 010 [arXiv:1410.4466] [INSPIRE].
A.F. Faedo, D. Mateos and J. Tarrío, Three-dimensional super Yang-Mills with unquenched flavor, JHEP 07 (2015) 056 [arXiv:1505.00210] [INSPIRE].
A.F. Faedo, A. Kundu, D. Mateos, C. Pantelidou and J. Tarrío, Three-dimensional super Yang-Mills with compressible quark matter, JHEP 03 (2016) 154 [arXiv:1511.05484] [INSPIRE].
A.F. Faedo, D. Mateos, C. Pantelidou and J. Tarrío, Unquenched flavor on the Higgs branch, JHEP 11 (2016) 021 [arXiv:1607.07773] [INSPIRE].
D. Areán, I. Iatrakis, M. Järvinen and E. Kiritsis, The discontinuities of conformal transitions and mass spectra of V-QCD, JHEP 11 (2013) 068 [arXiv:1309.2286] [INSPIRE].
T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis, C. Rosen and K. Tuominen, A holographic model for QCD in the Veneziano limit at finite temperature and density, JHEP 04 (2014) 124 [Erratum ibid. 1502 (2015) 033] [arXiv:1312.5199] [INSPIRE].
T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis and K. Tuominen, Quantum and stringy corrections to the equation of state of holographic QCD matter and the nature of the chiral transition, Phys. Rev. D 91 (2015) 055017 [arXiv:1501.06379] [INSPIRE].
M. Järvinen, Massive holographic QCD in the Veneziano limit, JHEP 07 (2015) 033 [arXiv:1501.07272] [INSPIRE].
R. Rougemont, R. Critelli and J. Noronha, Holographic calculation of the QCD crossover temperature in a magnetic field, Phys. Rev. D 93 (2016) 045013 [arXiv:1505.07894] [INSPIRE].
T. Drwenski, U. Gürsoy and I. Iatrakis, Thermodynamics and CP-odd transport in Holographic QCD with Finite Magnetic Field, JHEP 12 (2016) 049 [arXiv:1506.01350] [INSPIRE].
M. Järvinen, Holography and the conformal window in the Veneziano limit, arXiv:1508.00685 [INSPIRE].
U. Gürsoy, I. Iatrakis, M. Järvinen and G. Nijs, Inverse Magnetic Catalysis from improved Holographic QCD in the Veneziano limit, arXiv:1611.06339 [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic Brane Solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
S.S. Pal, Fermi-like Liquid From Einstein-DBI-Dilaton System, JHEP 04 (2013) 007 [arXiv:1209.3559] [INSPIRE].
J. Tarrío, Transport properties of spacetime-filling branes, JHEP 04 (2014) 042 [arXiv:1312.2902] [INSPIRE].
M. Cataldo and A. Garcia, Three dimensional black hole coupled to the Born-Infeld electrodynamics, Phys. Lett. B 456 (1999) 28 [hep-th/9903257] [INSPIRE].
S. Fernando and D. Krug, Charged black hole solutions in Einstein-Born-Infeld gravity with a cosmological constant, Gen. Rel. Grav. 35 (2003) 129 [hep-th/0306120] [INSPIRE].
T.K. Dey, Born-Infeld black holes in the presence of a cosmological constant, Phys. Lett. B 595 (2004) 484 [hep-th/0406169] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
K. Jensen, Chaos in AdS 2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
N. Iizuka, S. Kachru, N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Bianchi Attractors: A Classification of Extremal Black Brane Geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
N. Iizuka et al., Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes and a Classification for the Homogeneous Case, JHEP 03 (2013) 126 [arXiv:1212.1948] [INSPIRE].
S. Kachru, N. Kundu, A. Saha, R. Samanta and S.P. Trivedi, Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes, JHEP 03 (2014) 074 [arXiv:1310.5740] [INSPIRE].
E. D’Hoker and P. Kraus, Charged Magnetic Brane Solutions in AdS (5) and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic Field Induced Quantum Criticality via new Asymptotically AdS 5 Solutions, Class. Quant. Grav. 27 (2010) 215022 [arXiv:1006.2573] [INSPIRE].
V.G. Filev, C.V. Johnson, R.C. Rashkov and K.S. Viswanathan, Flavoured large-N gauge theory in an external magnetic field, JHEP 10 (2007) 019 [hep-th/0701001] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Finite temperature large-N gauge theory with quarks in an external magnetic field, JHEP 07 (2008) 080 [arXiv:0709.1547] [INSPIRE].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [INSPIRE].
O. Bergman, G. Lifschytz and M. Lippert, Response of Holographic QCD to Electric and Magnetic Fields, JHEP 05 (2008) 007 [arXiv:0802.3720] [INSPIRE].
C.V. Johnson and A. Kundu, External Fields and Chiral Symmetry Breaking in the Sakai-Sugimoto Model, JHEP 12 (2008) 053 [arXiv:0803.0038] [INSPIRE].
M.S. Alam, V.S. Kaplunovsky and A. Kundu, Chiral Symmetry Breaking and External Fields in the Kuperstein-Sonnenschein Model, JHEP 04 (2012) 111 [arXiv:1202.3488] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
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Kundu, A., Kundu, N. Fundamental flavours, fields and fixed points: a brief account. J. High Energ. Phys. 2017, 71 (2017). https://doi.org/10.1007/JHEP03(2017)071
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DOI: https://doi.org/10.1007/JHEP03(2017)071