Abstract
We argue that a SO(d) magnetic monopole in an asymptotically AdS space-time is dual to a d-dimensional strongly coupled system in a solid state. In light of this, it would be remiss of us not to dub such a field configuration solidon. In the presence of mixed boundary conditions, a solidon spontaneously breaks translations (among many other symmetries) and gives rise to Goldstone excitations on the boundary — the phonons of the solid. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the mixed boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solidon for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find such free energy to be lower than that of thermal AdS. This suggests that our solidon undergoes a solid-to-liquid first order phase transition by melting into a Schwarzschild-AdS black hole as the temperature is raised.
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J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].
J. de Boer, M.P. Heller and N. Pinzani-Fokeeva, Effective actions for relativistic fluids from holography, JHEP 08 (2015) 086 [arXiv:1504.07616] [INSPIRE].
M. Crossley, P. Glorioso, H. Liu and Y. Wang, Off-shell hydrodynamics from holography, JHEP 02 (2016) 124 [arXiv:1504.07611] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009)105007 [arXiv:0908.1972] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
A. Esposito, S. Garcia-Saenz and R. Penco, First sound in holographic superfluids at zero temperature, JHEP 12 (2016) 136 [arXiv:1606.03104] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
A. Buchel and C. Pagnutti, Exotic Hairy Black Holes, Nucl. Phys. B 824 (2010) 85 [arXiv:0904.1716] [INSPIRE].
D.E. Soper, Classical Field Theory, Dover Publications, Mineola U.S.A. (1976).
H. Leutwyler, Phonons as goldstone bosons, Helv. Phys. Acta 70 (1997) 275 [hep-ph/9609466] [INSPIRE].
D.T. Son, Effective Lagrangian and topological interactions in supersolids, Phys. Rev. Lett. 94 (2005) 175301 [cond-mat/0501658] [INSPIRE].
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025 [hep-th/0512260] [INSPIRE].
S. Endlich, A. Nicolis and J. Wang, Solid Inflation, JCAP 10 (2013) 011 [arXiv:1210.0569] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
A.R. Lugo, E.F. Moreno and F.A. Schaposnik, Monopole solutions in AdS space, Phys. Lett. B 473 (2000) 35 [hep-th/9911209] [INSPIRE].
A.R. Lugo and F.A. Schaposnik, Monopole and dyon solutions in AdS space, Phys. Lett. B 467 (1999) 43 [hep-th/9909226] [INSPIRE].
S. Bolognesi and D. Tong, Monopoles and Holography, JHEP 01 (2011) 153 [arXiv:1010.4178] [INSPIRE].
P. Sutcliffe, Monopoles in AdS, JHEP 08 (2011) 032 [arXiv:1104.1888] [INSPIRE].
L. Alberte, M. Baggioli, A. Khmelnitsky and O. Pujolàs, Solid Holography and Massive Gravity, JHEP 02 (2016) 114 [arXiv:1510.09089] [INSPIRE].
L. Alberte, M. Baggioli and O. Pujolàs, Viscosity bound violation in holographic solids and the viscoelastic response, JHEP 07 (2016) 074 [arXiv:1601.03384] [INSPIRE].
L. Alberte, M. Ammon, M. Baggioli, A. Jiménez and O. Pujolàs, Black hole elasticity and gapped transverse phonons in holography, arXiv:1708.08477 [INSPIRE].
J. Kang and A. Nicolis, Platonic solids back in the sky: Icosahedral inflation, JCAP 03 (2016) 050 [arXiv:1509.02942] [INSPIRE].
A. Nicolis, R. Penco and R.A. Rosen, Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction, Phys. Rev. D 89 (2014) 045002 [arXiv:1307.0517] [INSPIRE].
I. Low and A.V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602 [hep-th/0110285] [INSPIRE].
L. Alberte, Massive Gravity on Curved Background, Int. J. Mod. Phys. D 21 (2012) 1250058 [arXiv:1110.3818] [INSPIRE].
E.J. Weinberg, Classical solutions in quantum field theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2015).
I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].
T. Faulkner, G.T. Horowitz and M.M. Roberts, New stability results for Einstein scalar gravity, Class. Quant. Grav. 27 (2010) 205007 [arXiv:1006.2387] [INSPIRE].
T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, JHEP 04 (2011) 051 [arXiv:1008.1581] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
S. Weinberg, The Quantum Theory of Fields. Vol. 2: Modern Applications, Cambridge University Press, Cambridge U.K. (1995).
R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudoGoldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. 115B (1982) 197 [INSPIRE].
L. Landau and E. Lifshitz, Course of theoretical physics. Vol. 5: Statistical Physics, Pergamon Press, Oxford U.K. (1968).
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
M. Natsuume, Lecture Notes in Physics. Vol. 903: AdS/CFT Duality User Guide, Springer, Berlin Germany (2015).
S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A General class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
E. Inonu and E.P. Wigner, On the Contraction of Groups and Their Representations, Proc. Nat. Acad. Sci. 39 (1953) 510.
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].
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Esposito, A., Garcia-Saenz, S., Nicolis, A. et al. Conformal solids and holography. J. High Energ. Phys. 2017, 113 (2017). https://doi.org/10.1007/JHEP12(2017)113
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DOI: https://doi.org/10.1007/JHEP12(2017)113