Abstract
We use a Weyl transformation between S1 × Sd−1 and \( {S}^1\times {\mathrm{\mathscr{H}}}^{d-1}/\mathbb{Z} \) to relate a conformal field theory at arbitrary temperature on Sd−1 to itself at the inverse temperature on \( {\mathrm{\mathscr{H}}}^{d-1}/\mathbb{Z} \). We use this equivalence to deduce a confining phase transition at finite temperature for large-N gauge theories on hyperbolic space. In the context of gauge/gravity duality, this equivalence provides new examples of smooth bulk solutions which asymptote to conically singular geometries at the AdS boundary. We also discuss implications for the Eguchi-Kawai mechanism and a high-temperature/low-temperature duality on Sd−1.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
E. Shaghoulian, Modular forms and a generalized Cardy formula in higher dimensions, Phys. Rev. D 93 (2016) 126005 [arXiv:1508.02728] [INSPIRE].
A. Belin et al., Universality of sparse d < 2 conformal field theory at large-N, JHEP 03 (2017) 067 [arXiv:1610.06186] [INSPIRE].
E. Shaghoulian, Modular invariance of conformal field theory on S 1 × S 3 and circle fibrations, Phys. Rev. Lett. 119 (2017) 131601 [arXiv:1612.05257] [INSPIRE].
G.H. Wannier, The statistical problem in cooperative phenomena, Rev. Mod. Phys. 17 (1945) 50 [INSPIRE].
R.M.F.Houtappel, Order-disorder in hexagonal lattices, Physica 16 (1950) 425.
K. Husimi and I. Syôzi, The statistics of honeycomb and triangular lattice. I, Prog. Theor. Phys. 5 (1950) 177.
G.H. Wannier, Antiferromagnetism. The triangular Ising net, Phys. Rev. 79 (1950) 357 [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of black holes in Anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
D. Marolf, M. Rangamani and M. Van Raamsdonk, Holographic models of de Sitter QFTs, Class. Quant. Grav. 28 (2011) 105015 [arXiv:1007.3996] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
J. Camps, Gravity duals of boundary cones, JHEP 09 (2016) 139 [arXiv:1605.08588] [INSPIRE].
D. Birmingham and M. Rinaldi, Bubbles in Anti-de Sitter space, Phys. Lett. B 544 (2002) 316 [hep-th/0205246] [INSPIRE].
V. Balasubramanian and S.F. Ross, The dual of nothing, Phys. Rev. D 66 (2002) 086002 [hep-th/0205290] [INSPIRE].
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [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].
T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].
O.J.C. Dias et al., A scalar field condensation instability of rotating anti-de Sitter black holes, JHEP 11 (2010) 036 [arXiv:1007.3745] [INSPIRE].
A. Belin, A. Maloney and S. Matsuura, Holographic phases of Renyi entropies, JHEP 12 (2013) 050 [arXiv:1306.2640] [INSPIRE].
A. Belin and A. Maloney, A new instability of the topological black hole, Class. Quant. Grav. 33 (2016) 215003 [arXiv:1412.0280] [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].
J.A. Hutasoit, S.P. Kumar and J. Rafferty, Real time response on dS 3 : the topological AdS black hole and the bubble, JHEP 04 (2009) 063 [arXiv:0902.1658] [INSPIRE].
T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory, Phys. Rev. Lett. 48 (1982) 1063 [INSPIRE].
P. Kovtun, M. Ünsal and L.G. Yaffe, Volume independence in large-N c QCD-like gauge theories, JHEP 06 (2007) 019 [hep-th/0702021] [INSPIRE].
E. Shaghoulian, Emergent gravity from Eguchi-Kawai reduction, JHEP 03 (2017) 011 [arXiv:1611.04189] [INSPIRE].
B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations, Commun. Math. Phys. 10 (1968) 280 [INSPIRE].
S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
E. Shaghoulian, Nonlocal operators in CFT, to be published.
D. Kutasov and F. Larsen, Partition sums and entropy bounds in weakly coupled CFT, JHEP 01 (2001) 001 [hep-th/0009244] [INSPIRE].
Y. Chen, Y.-K. Lim and E. Teo, Deformed hyperbolic black holes, Phys. Rev. D 92 (2015) 044058 [arXiv:1507.02416] [INSPIRE].
D. Klemm, V. Moretti and L. Vanzo, Rotating topological black holes, Phys. Rev. D 57 (1998) 6127 [Erratum ibid. D 60 (1999) 109902] [gr-qc/9710123] [INSPIRE].
W. Thurston, Geometry and topology of three-manifolds, Princeton lecture notes, http://library.msri.org/books/gt3m (1980).
D. Cooper et al., Three-dimensional orbifolds and cone-manifolds, The Mathematical Society of Japan, Tokyo Japan (2000).
W.D. Dunbar, Geometric orbifolds, Rev. Mat. Univ. Complut. Madrid 1 (1988) 67, http://eudml.org/doc/43193.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1709.06084
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Horowitz, G.T., Shaghoulian, E. Detachable circles and temperature-inversion dualities for CFT d . J. High Energ. Phys. 2018, 135 (2018). https://doi.org/10.1007/JHEP01(2018)135
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2018)135