Abstract
Four dimensional gauge theories in anti-de Sitter space, including pure Yang-Mills theory, exhibit a quantum phase transition between a deconfined phase and a confined phase as the gauge coupling is varied. We explore various mechanisms by which this may occur, both in a fixed background and in the presence of gravity. We also make a number of observations on the dynamics of four dimensional supersymmetric gauge theories in anti-de Sitter space.
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References
J. Greensite, An introduction to the confinement problem, Lect. Notes Phys. 821 (2011) 1 [INSPIRE].
C.G. Callan Jr. and F. Wilczek, Infrared behavior at negative curvature, Nucl. Phys. B 340 (1990) 366 [INSPIRE].
A.M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
M. Ünsal, Abelian duality, confinement, and chiral symmetry breaking in a SU(2) QCD-like theory, Phys. Rev. Lett. 100 (2008) 032005 [arXiv:0708.1772] [INSPIRE].
M. Ünsal, Magnetic bion condensation: a new mechanism of confinement and mass gap in four dimensions, Phys. Rev. D 80 (2009) 065001 [arXiv:0709.3269] [INSPIRE].
M. Shifman and M. Ünsal, QCD-like theories on R 3 × S 1 : a smooth journey from small to large r(S 1) with double-trace deformations, Phys. Rev. D 78 (2008) 065004 [arXiv:0802.1232] [INSPIRE].
M. Ünsal and L.G. Yaffe, Center-stabilized Yang-Mills theory: confinement and large-N volume independence, Phys. Rev. D 78 (2008) 065035 [arXiv:0803.0344] [INSPIRE].
E. Poppitz and M. Ünsal, Conformality or confinement (II): one-flavor CFTs and mixed-representation QCD, JHEP 12 (2009) 011 [arXiv:0910.1245] [INSPIRE].
E. Poppitz and M. Ünsal, Seiberg-Witten and ‘Polyakov-like’ magnetic bion confinements are continuously connected, JHEP 07 (2011) 082 [arXiv:1105.3969] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [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].
D. Marolf and S.F. Ross, Boundary conditions and new dualities: vector fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].
S.W. Hawking and S.F. Ross, Duality between electric and magnetic black holes, Phys. Rev. D 52 (1995) 5865 [hep-th/9504019] [INSPIRE].
E. Witten, SL(2, \( \mathbb{Z} \)) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
I.R. Klebanov, J.M. Maldacena and C.B. Thorn, Dynamics of flux tubes in large N gauge theories, JHEP 04 (2006) 024 [hep-th/0602255] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
O. Aharony, D. Marolf and M. Rangamani, Conformal field theories in anti-de Sitter space, JHEP 02 (2011) 041 [arXiv:1011.6144] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B.C. van Rees, A natural language for AdS/CFT correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].
M.F. Paulos, Towards Feynman rules for Mellin amplitudes, JHEP 10 (2011) 074 [arXiv:1107.1504] [INSPIRE].
R. Logayanagam, Bulk confinement of a boundary symmetry, talk given at the Chandrasekhar Discussion Meeting, ICTS, Mumbai India, Mar 2011, http://www.icts.res.in/media/uploads/Talk/Slides/DamThanh/22march/logayanagam.pdf.
S.W. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [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].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [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].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
O. Aharony, Y.E. Antebi and M. Berkooz, Open string moduli in KKLT compactifications, Phys. Rev. D 72 (2005) 106009 [hep-th/0508080] [INSPIRE].
J. Polchinski and E. Silverstein, Dual purpose landscaping tools: small extra dimensions in AdS/CFT, arXiv:0908.0756 [INSPIRE].
B. Zumino, Nonlinear realization of supersymmetry in de Sitter space, Nucl. Phys. B 127 (1977) 189 [INSPIRE].
E.A. Ivanov and A.S. Sorin, Superfield formulation of Osp(1, 4) supersymmetry, J. Phys. A 13 (1980) 1159 [INSPIRE].
N. Sakai and Y. Tanii, Supersymmetry and vacuum energy in anti-de Sitter space, Phys. Lett. B 146 (1984) 38 [INSPIRE].
C.P. Burgess, Supersymmetry breaking and vacuum energy on anti-de Sitter space, Nucl. Phys. B 259 (1985) 473 [INSPIRE].
C.P. Burgess and C.A. Lütken, Propagators and effective potentials in anti-de Sitter space, Phys. Lett. B 153 (1985) 137 [INSPIRE].
C.J.C. Burges, D.Z. Freedman, S. Davis and G.W. Gibbons, Supersymmetry in anti-de Sitter space, Annals Phys. 167 (1986) 285 [INSPIRE].
A. Adams, H. Jockers, V. Kumar and J.M. Lapan, N = 1 σ-models in AdS 4, JHEP 12 (2011) 042 [arXiv:1104.3155] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
B. Allen and C.A. Lütken, Spinor two point functions in maximally symmetric spaces, Commun. Math. Phys. 106 (1986) 201 [INSPIRE].
B. Gripaios, H.D. Kim, R. Rattazzi, M. Redi and C. Scrucca, Gaugino mass in AdS space, JHEP 02 (2009) 043 [arXiv:0811.4504] [INSPIRE].
M. Porrati and L. Girardello, The three dimensional dual of 4D chirality, JHEP 11 (2009) 114 [arXiv:0908.3487] [INSPIRE].
G. Veneziano and S. Yankielowicz, An effective Lagrangian for the pure N = 1 supersymmetric Yang-Mills theory, Phys. Lett. B 113 (1982) 231 [INSPIRE].
I.I. Kogan, A. Kovner and M.A. Shifman, More on supersymmetric domain walls, N counting and glued potentials, Phys. Rev. D 57 (1998) 5195 [hep-th/9712046] [INSPIRE].
S. Bolognesi and D. Tong, Magnetic catalysis in AdS 4, Class. Quant. Grav. 29 (2012) 194003 [arXiv:1110.5902] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev. D 84 (2011) 126003 [arXiv:1106.1870] [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].
D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the θ-angle in N =4 super Yang-Mills theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
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].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact terms, unitarity and F-maximization in three-dimensional superconformal theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [INSPIRE].
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Aharony, O., Berkooz, M., Tong, D. et al. Confinement in anti-de Sitter space. J. High Energ. Phys. 2013, 76 (2013). https://doi.org/10.1007/JHEP02(2013)076
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DOI: https://doi.org/10.1007/JHEP02(2013)076