Abstract
We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in ferromagnets. The black-hole phase corresponds to the ordered and the graviton gas corresponds to the disordered phases respectively. A simple set-up based on Einstein-dilaton gravity indicates that the vicinity of the phase transition is governed by a linear-dilaton CFT. Employing this CFT we calculate scaling of observables near T c , and obtain mean-field scaling in a semi-classical approximation. In case of the XY model the Goldstone mode is identified with the zero mode of the NS-NS two-form. We show that the second speed of sound vanishes at the transition also with the mean field exponent.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [SPIRES].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [SPIRES].
S. Sachdev, Quantum phase transitions, Cambridge University Press, Cambridge U.K. (1999).
A.M. Polyakov, Thermal properties of gauge fields and quark liberation, Phys. Lett. B 72 (1978) 477 [SPIRES].
L. Susskind, Lattice models of quark confinement at high temperature, Phys. Rev. D 20 (1979) 2610 [SPIRES].
B. Svetitsky and L.G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys. B 210 (1982) 423 [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].
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] [SPIRES].
U. Gürsoy, Continuous Hawking-page transitions in Einstein-scalar gravity, arXiv:1007.0500 [SPIRES].
J. Polchinski, String theory vol. I, Cambridge University Press, Cambridge U.K. (1998).
J.J. Atick and E. Witten, The Hagedorn transition and the number of degrees of freedom of string theory, Nucl. Phys. B 310 (1988) 291 [SPIRES].
H. Pfeiffer and R. Oeckl, The dual of non-Abelian lattice gauge theory, Nucl. Phys. Proc. Suppl. 106 (2002) 1010 [hep-lat/0110034] [SPIRES].
R. Fiore, A. Papa and P. Provero, Spectrum of screening masses in the (3+1)D SU(2) pure gauge theory near the critical temperature, Nucl. Phys. Proc. Suppl. 119 (2003) 490 [hep-lat/0208020] [SPIRES].
O. Aharony and E. Witten, Anti-de Sitter space and the center of the gauge group, JHEP 11 (1998) 018 [hep-th/9807205] [SPIRES].
F.R. Brown and L.G. Yaffe, The coherent state variational algorithm: a numerical method for solving large-N gauge theories, Nucl. Phys. B 271 (1986) 267 [SPIRES].
T.A. Dickens, U.J. Lindqwister, W.R. Somsky, L.G. Yaffe, The coherent state variational algorithm. 2. Implementation and testing., Nucl. Phys. B 309 (1988) 1 [SPIRES].
R.D. Pisarski and M. Tytgat, Why the SU(infinity) deconfining phase transition might be of second order, hep-ph/9702340 [SPIRES].
J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [SPIRES].
V.L. Berezinsky, Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. 1. Classical systems, Sov. Phys. JETP 32 (1971) 493 [SPIRES].
J.M. Kosterlitz, The critical properties of the two-dimensional xy model, J. Phys. C 7 (1974) 1046 [SPIRES].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Deconfinement and gluon plasma dynamics in improved holographic QCD, Phys. Rev. Lett. 101 (2008) 181601 [arXiv:0804.0899] [SPIRES].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and thermodynamics of 5D dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [SPIRES].
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] [SPIRES].
N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv:1003.0010] [SPIRES].
A.H. Chamseddine, A study of noncritical strings in arbitrary dimensions, Nucl. Phys. B 368 (1992) 98 [SPIRES].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [SPIRES].
R.C. Myers, New dimensions for old strings, Phys. Lett. B 199 (1987) 371 [SPIRES].
M. Headrick, Hedgehog black holes and the Polyakov loop at strong coupling, Phys. Rev. D 77 (2008) 105017 [arXiv:0712.4155] [SPIRES].
S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [SPIRES].
A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature, Phys. Lett. B 434 (1998) 36 [hep-th/9803137] [SPIRES].
D. Bak, A. Karch and L.G. Yaffe, Debye screening in strongly coupled N = 4 supersymmetric Yang-Mills plasma, JHEP 08 (2007) 049 [arXiv:0705.0994] [SPIRES].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [SPIRES].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [SPIRES].
M.B. Green, J.H. Schwarz and E. Witten, Superstring theory vol.1, Cambridge University Press, Cambridge U.K. (1987).
G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1 [SPIRES].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [SPIRES].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [SPIRES].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [SPIRES].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small hairy black holes in AdS 5 × S 5, arXiv:1005.1287 [SPIRES].
P. Basu et al., Small hairy black holes in global AdS spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [SPIRES].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [SPIRES].
I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [SPIRES].
D.T. Son, Hydrodynamics of relativistic systems with broken continuous symmetries, Int. J. Mod. Phys. A 16S1C (2001) 1284 [hep-ph/0011246] [SPIRES].
S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [SPIRES].
H.T.C. Stoof, K.B. Gubbels and D.B.M Dickersheid, Ultracold quantum fields, Springer (2009).
N.D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17 (1966) 1133 [SPIRES].
P.C. Hohenberg, Existence of long-range order in one and two dimensions, Phys. Rev. 158 (1967) 383 [SPIRES].
S.R. Coleman, There are no Goldstone bosons in two-dimensions, Commun. Math. Phys. 31 (1973) 259 [SPIRES].
Y. Kinar, E. Schreiber and J. Sonnenschein, \( Q\;\bar{Q} \) potential from strings in curved spacetime: classical results, Nucl. Phys. B 566 (2000) 103 [hep-th/9811192] [SPIRES].
U. Gürsoy, E. Kiritsis, G. Michalogiorgakis and F. Nitti, Thermal transport and drag force in improved holographic QCD, JHEP 12 (2009) 056 [arXiv:0906.1890] [SPIRES].
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Gürsoy, U. Gravity/spin-model correspondence and holographic superfluids. J. High Energ. Phys. 2010, 62 (2010). https://doi.org/10.1007/JHEP12(2010)062
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DOI: https://doi.org/10.1007/JHEP12(2010)062