Flavoured large \(N\) gauge theory on a compact space with an external magnetic field. (English) Zbl 1342.81280
Summary: The phase structure of flavoured \(N = 2\) SYM on a three sphere in an external magnetic field is studied. The pairing effect of the magnetic field competes with the dissociating effect of the Casimir energy, leading to an interesting phase structure of confined and deconfined phases separated by a critical curve of a first order quantum phase transition. At vanishing magnetic field the phase transition is of a third order. For sufficiently strong magnetic field, the only stable phase is the confined phase and magnetic catalysis of chiral symmetry breaking is realized. The meson spectra of the theory exhibit Zeeman splitting and level crossing and feature a finite jump at the phase transition between the confined and deconfined phases. At strong magnetic field the ground state has a massless mode corresponding to the Goldstone boson associated with the spontaneously broken \(U(1)\) R-symmetry analogous to the {\(\eta\)} meson in QCD.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
References:
| [1] | V. Gusynin, V. Miransky and I. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2 + 1)-dimensions, Phys. Rev. Lett. 73 (1994) 3499 [Erratum ibid.76 (1996) 1005] [hep-ph/9405262] [INSPIRE]. |
| [2] | V. Gusynin, V. Miransky and I. Shovkovy, Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in (3 + 1)-dimensions, Phys. Lett.B 349 (1995) 477 [hep-ph/9412257] [INSPIRE]. |
| [3] | D.K. Hong, Y. Kim and S.-J. Sin, RG analysis of magnetic catalysis in dynamical symmetry breaking, Phys. Rev. D 54 (1996) 7879 [hep-th/9603157] [INSPIRE]. |
| [4] | K. Klimenko, Three-dimensional Gross-Neveu model in an external magnetic field, Theor. Math. Phys. 89 (1992) 1161 [Teor. Mat. Fiz.89 (1991) 211] [INSPIRE]. |
| [5] | K. Klimenko, Three-dimensional Gross-Neveu model at nonzero temperature and in an external magnetic field, Z. Phys. C 54 (1992) 323 [INSPIRE]. |
| [6] | K. Klimenko, Three-dimensional Gross-Neveu model at nonzero temperature and in an external magnetic field, Theor. Math. Phys. 90 (1992) 1 [Teor. Mat. Fiz.90 (1992) 3] [INSPIRE]. |
| [7] | 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]. · Zbl 0914.53047 |
| [8] | A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP06 (2002) 043 [hep-th/0205236] [INSPIRE]. · doi:10.1088/1126-6708/2002/06/043 |
| [9] | V.G. Filev, C.V. Johnson, R. Rashkov and K. Viswanathan, Flavoured large-N gauge theory in an external magnetic field, JHEP10 (2007) 019 [hep-th/0701001] [INSPIRE]. · doi:10.1088/1126-6708/2007/10/019 |
| [10] | V.G. Filev and D. Zoakos, Towards unquenched holographic magnetic catalysis, JHEP08 (2011) 022 [arXiv:1106.1330] [INSPIRE]. · Zbl 1298.81277 · doi:10.1007/JHEP08(2011)022 |
| [11] | J. Erdmenger, V.G. Filev and D. Zoakos, Magnetic catalysis with massive dynamical flavours, JHEP08 (2012) 004 [arXiv:1112.4807] [INSPIRE]. · doi:10.1007/JHEP08(2012)004 |
| [12] | M. Ammon, V.G. Filev, J. Tarrio and D. Zoakos, D3/D7 quark-gluon plasma with magnetically induced anisotropy, JHEP09 (2012) 039 [arXiv:1207.1047] [INSPIRE]. · doi:10.1007/JHEP09(2012)039 |
| [13] | A. Karch and A. O’Bannon, Chiral transition of N = 4 super Yang-Mills with flavor on a 3-sphere, Phys. Rev. D 74 (2006) 085033 [hep-th/0605120] [INSPIRE]. |
| [14] | A. Karch, A. O’Bannon and L.G. Yaffe, Critical exponents from AdS/CFT with flavor, JHEP09 (2009) 042 [arXiv:0906.4959] [INSPIRE]. · doi:10.1088/1126-6708/2009/09/042 |
| [15] | J. Erdmenger and V. Filev, Mesons from global Anti-de Sitter space, JHEP01 (2011) 119 [arXiv:1012.0496] [INSPIRE]. · Zbl 1214.81208 · doi:10.1007/JHEP01(2011)119 |
| [16] | S.P. Kumar, Spinning flavour branes and fermion pairing instabilities, Phys. Rev.D 84 (2011) 026003 [arXiv:1104.1405] [INSPIRE]. |
| [17] | S. Chunlen, K. Peeters, P. Vanichchapongjaroen and M. Zamaklar, Instability of N = 2 gauge theory in compact space with an isospin chemical potential, JHEP01 (2013) 035 [arXiv:1210.6188] [INSPIRE]. · Zbl 1342.81269 · doi:10.1007/JHEP01(2013)035 |
| [18] | M. Gell-Mann, R.J. Oakes and B. Renner, Behavior of current divergences under SU(3) × SU(3), Phys. Rev. 175 (1968) 2195 [INSPIRE]. · doi:10.1103/PhysRev.175.2195 |
| [19] | A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP04 (2006) 015 [hep-th/0512125] [INSPIRE]. · doi:10.1088/1126-6708/2006/04/015 |
| [20] | V.G. Filev and C.V. Johnson, Universality in the large-Ncdynamics of flavour: thermal vs. quantum induced phase transitions, JHEP10 (2008) 058 [arXiv:0805.1950] [INSPIRE]. · doi:10.1088/1126-6708/2008/10/058 |
| [21] | D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP05 (2007) 067 [hep-th/0701132] [INSPIRE]. · doi:10.1088/1126-6708/2007/05/067 |
| [22] | D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE]. · Zbl 1228.81236 · doi:10.1103/PhysRevLett.97.091601 |
| [23] | V.P. Frolov, Merger transitions in brane-black-hole systems: criticality, scaling and self-similarity, Phys. Rev. D 74 (2006) 044006 [gr-qc/0604114] [INSPIRE]. |
| [24] | T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Finite temperature large-N gauge theory with quarks in an external magnetic field, JHEP07 (2008) 080 [arXiv:0709.1547] [INSPIRE]. · doi:10.1088/1126-6708/2008/07/080 |
| [25] | J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP12 (2007) 091 [arXiv:0709.1551] [INSPIRE]. · Zbl 1246.81237 · doi:10.1088/1126-6708/2007/12/091 |
| [26] | V.G. Filev, C.V. Johnson and J.P. Shock, Universal holographic chiral dynamics in an external magnetic field, JHEP08 (2009) 013 [arXiv:0903.5345] [INSPIRE]. · doi:10.1088/1126-6708/2009/08/013 |
| [27] | D. Arean, A. Paredes and A.V. Ramallo, Adding flavor to the gravity dual of non-commutative gauge theories, JHEP08 (2005) 017 [hep-th/0505181] [INSPIRE]. · doi:10.1088/1126-6708/2005/08/017 |
| [28] | M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP07 (2003) 049 [hep-th/0304032] [INSPIRE]. · doi:10.1088/1126-6708/2003/07/049 |
| [29] | N.J. Evans and J.P. Shock, Chiral dynamics from AdS space, Phys. Rev.D 70 (2004) 046002 [hep-th/0403279] [INSPIRE]. |
| [30] | R.C. Myers and R.M. Thomson, Holographic mesons in various dimensions, JHEP09 (2006) 066 [hep-th/0605017] [INSPIRE]. · doi:10.1088/1126-6708/2006/09/066 |
| [31] | V.G. Filev, Criticality, scaling and chiral symmetry breaking in external magnetic field, JHEP04 (2008) 088 [arXiv:0706.3811] [INSPIRE]. · doi:10.1088/1126-6708/2008/04/088 |
| [32] | 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]. |
| [33] | C.V. Johnson and A. Kundu, External fields and chiral symmetry breaking in the Sakai-Sugimoto model, JHEP12 (2008) 053 [arXiv:0803.0038] [INSPIRE]. · Zbl 1329.81268 · doi:10.1088/1126-6708/2008/12/053 |
| [34] | O. Bergman, G. Lifschytz and M. Lippert, Response of holographic QCD to electric and magnetic fields, JHEP05 (2008) 007 [arXiv:0802.3720] [INSPIRE]. · doi:10.1088/1126-6708/2008/05/007 |
| [35] | O. Bergman, G. Lifschytz and M. Lippert, Magnetic properties of dense holographic QCD, Phys. Rev. D 79 (2009) 105024 [arXiv:0806.0366] [INSPIRE]. |
| [36] | A. Zayakin, QCD vacuum properties in a magnetic field from AdS/CFT: chiral condensate and Goldstone mass, JHEP07 (2008) 116 [arXiv:0807.2917] [INSPIRE]. · doi:10.1088/1126-6708/2008/07/116 |
| [37] | V.G. Filev, Hot defect superconformal field theory in an external magnetic field, JHEP11 (2009) 123 [arXiv:0910.0554] [INSPIRE]. · doi:10.1088/1126-6708/2009/11/123 |
| [38] | N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Holographic description of the phase diagram of a chiral symmetry breaking gauge theory, JHEP03 (2010) 132 [arXiv:1002.1885] [INSPIRE]. · Zbl 1271.81174 · doi:10.1007/JHEP03(2010)132 |
| [39] | K. Jensen, A. Karch and E.G. Thompson, A holographic quantum critical point at finite magnetic field and finite density, JHEP05 (2010) 015 [arXiv:1002.2447] [INSPIRE]. · Zbl 1288.81114 · doi:10.1007/JHEP05(2010)015 |
| [40] | K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett.105 (2010) 041601 [arXiv:1002.3159] [INSPIRE]. · doi:10.1103/PhysRevLett.105.041601 |
| [41] | N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett. B 698 (2011) 91 [arXiv:1003.2694] [INSPIRE]. |
| [42] | V.G. Filev and R.C. Raskov, Magnetic catalysis of chiral symmetry breaking. A holographic prospective, Adv. High Energy Phys. 2010 (2010) 473206 [arXiv:1010.0444] [INSPIRE]. · Zbl 1216.81116 |
| [43] | C.B. Bayona, H. Boschi-Filho, M. Ihl and M.A. Torres, Pion and vector meson form factors in the Kuperstein-Sonnenschein holographic model, JHEP08 (2010) 122 [arXiv:1006.2363] [INSPIRE]. · Zbl 1290.81189 · doi:10.1007/JHEP08(2010)122 |
| [44] | M. Ihl, M.A. Torres, H. Boschi-Filho and C.B. Bayona, Scalar and vector mesons of flavor chiral symmetry breaking in the Klebanov-Strassler background, JHEP09 (2011) 026 [arXiv:1010.0993] [INSPIRE]. · Zbl 1301.81222 · doi:10.1007/JHEP09(2011)026 |
| [45] | N. Evans, A. Gebauer and K.-Y. Kim, E, B, μ, T phase structure of the D3/D7 holographic dual, JHEP05 (2011) 067 [arXiv:1103.5627] [INSPIRE]. · Zbl 1296.81135 · doi:10.1007/JHEP05(2011)067 |
| [46] | N. Callebaut, D. Dudal and H. Verschelde, Holographic ρ mesons in an external magnetic field, arXiv:1105.2217 [INSPIRE]. |
| [47] | S. Bolognesi and D. Tong, Magnetic catalysis in AdS4, Class. Quant. Grav.29 (2012) 194003 [arXiv:1110.5902] [INSPIRE]. · Zbl 1254.83028 · doi:10.1088/0264-9381/29/19/194003 |
| [48] | S. Bolognesi, J.N. Laia, D. Tong and K. Wong, A gapless hard wall: magnetic catalysis in bulk and boundary, JHEP07 (2012) 162 [arXiv:1204.6029] [INSPIRE]. · doi:10.1007/JHEP07(2012)162 |
| [49] | M. Sohaib Alam, M. Ihl, A. Kundu and S. Kundu, Back-reaction of non-supersymmetric probes: external fields and chemical potential, in preparation. |
| [50] | M. Ihl, A. Kundu and S. Kundu, Back-reaction of non-supersymmetric probes: phase transition and stability, JHEP12 (2012) 070 [arXiv:1208.2663] [INSPIRE]. · doi:10.1007/JHEP12(2012)070 |
| [51] | G. Bali et al., The QCD phase diagram for external magnetic fields, JHEP02 (2012) 044 [arXiv:1111.4956] [INSPIRE]. · Zbl 1309.81258 · doi:10.1007/JHEP02(2012)044 |
| [52] | C.P. Herzog, S.A. Stricker and A. Vuorinen, Hyperfine splitting and the Zeeman effect in holographic heavy-light mesons, Phys. Rev. D 82 (2010) 041701 [arXiv:1005.3285] [INSPIRE]. |
| [53] | M. Chernodub, Superconductivity of QCD vacuum in strong magnetic field, Phys. Rev.D 82 (2010) 085011 [arXiv:1008.1055] [INSPIRE]. |
| [54] | M. Chernodub, Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu-Jona-Lasinio model, Phys. Rev. Lett.106 (2011) 142003 [arXiv:1101.0117] [INSPIRE]. · doi:10.1103/PhysRevLett.106.142003 |
| [55] | V. Braguta, P. Buividovich, M. Chernodub and M. Polikarpov, Electromagnetic superconductivity of vacuum induced by strong magnetic field: numerical evidence in lattice gauge theory, Phys. Lett. B 718 (2012) 667 [arXiv:1104.3767] [INSPIRE]. |
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