Abstract
Gravitational instantons with NUT charge are magnetic monopoles upon dimensional reduction. We determine whether NUT charge can proliferate via the Polyakov mechanism and partially screen gravitational interactions. In semiclassical Einstein gravity, Taub-NUT instantons experience a universal attractive force in the path integral that prevents proliferation. This attraction further leads to semiclassical clumping instabilities, similar to the known instabilities of hot flat space and the Kaluza-Klein vacuum. Beyond pure Einstein gravity, NUT proliferation depends on the following question: is the mass of a gravitational instanton in the theory always greater than its NUT charge? Using spinorial methods we show that the answer to this question is ‘yes’ if all matter fields obey a natural Euclidean energy condition. Therefore, the attractive force between instantons in the path integral wins out and gravity is dynamically protected against screening. Semiclassical gravity with a compactified circle can be self-consistently quantum ordered, at the cost of suffering from clumping instabilities.
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References
X.-G. Wen, Quantum orders and symmetric spin liquids, Phys. Rev. B 65 (2002) 165113 [INSPIRE].
X.G. Wen, Quantum field theory of many-body systems: from the origin of sound to an origin of light and electrons, Oxford University Press, Oxford U.K. (2004) [INSPIRE].
S.-S. Lee, Emergence of gravity from interacting simplices, Int. J. Mod. Phys. A 24 (2009) 4271 [gr-qc/0609107] [INSPIRE].
Z.-C. Gu and X.-G. Wen, Emergence of helicity ±2 modes (gravitons) from qubit models, Nucl. Phys. B 863 (2012) 90 [arXiv:0907.1203] [INSPIRE].
C. Xu and P. Hořava, Emergent gravity at a Lifshitz point from a Bose liquid on the lattice, Phys. Rev. D 81 (2010) 104033 [arXiv:1003.0009] [INSPIRE].
S.-S. Lee, Holographic matter: deconfined string at criticality, Nucl. Phys. B 862 (2012) 781 [arXiv:1108.2253] [INSPIRE].
S.W. Hawking, Space-time foam, Nucl. Phys. B 144 (1978) 349 [INSPIRE].
S. Carlip, Dominant topologies in Euclidean quantum gravity, Class. Quant. Grav. 15 (1998) 2629 [gr-qc/9710114] [INSPIRE].
A.M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. B 59 (1975) 82 [INSPIRE].
J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [INSPIRE].
D.J. Gross, Is quantum gravity unpredictable?, Nucl. Phys. B 236 (1984) 349 [INSPIRE].
E. Witten, Instantons, the quark model and the 1/N expansion, Nucl. Phys. B 149 (1979) 285 [INSPIRE].
A.K. Gupta and M.B. Wise, Comment on wormhole correlations, Phys. Lett. B 218 (1989) 21 [INSPIRE].
A.K. Gupta, J. Hughes, J. Preskill and M.B. Wise, Magnetic wormholes and topological symmetry, Nucl. Phys. B 333 (1990) 195 [INSPIRE].
M. Hermele et al., Stability of U(1) spin liquids in two dimensions, Phys. Rev. B 70 (2004) 214437 [cond-mat/0404751].
M. Ünsal, Topological symmetry, spin liquids and CFT duals of Polyakov model with massless fermions, arXiv:0804.4664 [INSPIRE].
E. Dyer, M. Mezei and S.S. Pufu, Monopole taxonomy in three-dimensional conformal field theories, arXiv:1309.1160 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Classification of gravitational instanton symmetries, Commun. Math. Phys. 66 (1979) 291 [INSPIRE].
R.D. Sorkin, Kaluza-Klein monopole, Phys. Rev. Lett. 51 (1983) 87 [INSPIRE].
D.J. Gross and M.J. Perry, Magnetic monopoles in Kaluza-Klein theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].
T. Appelquist and A. Chodos, Quantum effects in Kaluza-Klein theories, Phys. Rev. Lett. 50 (1983) 141 [INSPIRE].
M.A. Rubin and B.D. Roth, Temperature effects in five-dimensional Kaluza-Klein theory, Nucl. Phys. B 226 (1983) 444 [INSPIRE].
D.J. Gross, M.J. Perry and L.G. Yaffe, Instability of flat space at finite temperature, Phys. Rev. D 25 (1982) 330 [INSPIRE].
E. Witten, Instability of the Kaluza-Klein vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
A.M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
S.W. Hawking, Gravitational instantons, Phys. Lett. A 60 (1977) 81 [INSPIRE].
G.W. Gibbons and M.J. Perry, New gravitational instantons and their interactions, Phys. Rev. D 22 (1980) 313 [INSPIRE].
C.J. Hunter, The action of instantons with nut charge, Phys. Rev. D 59 (1999) 024009 [gr-qc/9807010] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
S.W. Hawking and C.N. Pope, Symmetry breaking by instantons in supergravity, Nucl. Phys. B 146 (1978) 381 [INSPIRE].
R.E. Young, Semiclassical stability of asymptotically locally flat spaces, Phys. Rev. D 28 (1983) 2420 [INSPIRE].
E.B. Bogomolny, Calculation of instanton-anti-instanton contributions in quantum mechanics, Phys. Lett. B 91 (1980) 431 [INSPIRE].
D.N. Page, Taub-NUT instanton with an horizon, Phys. Lett. B 78 (1978) 249 [INSPIRE].
D. Brill and H. Pfister, States of negative total energy in Kaluza-Klein theory, Phys. Lett. B 228 (1989) 359 [INSPIRE].
D. Brill and G.T. Horowitz, Negative energy in string theory, Phys. Lett. B 262 (1991) 437 [INSPIRE].
M.A. Rubin and B.D. Roth, Fermions and stability in five-dimensional Kaluza-Klein theory, Phys. Lett. B 127 (1983) 55 [INSPIRE].
R. Schon and S.-T. Yau, On the proof of the positive mass conjecture in general relativity, Commun. Math. Phys. 65 (1979) 45 [INSPIRE].
E. Witten, A simple proof of the positive energy theorem, Commun. Math. Phys. 80 (1981) 381 [INSPIRE].
G.W. Gibbons, S.W. Hawking, G.T. Horowitz and M.J. Perry, Positive mass theorems for black holes, Commun. Math. Phys. 88 (1983) 295 [INSPIRE].
T. Parker and C.H. Taubes, On Witten’s proof of the positive energy theorem, Commun. Math. Phys. 84 (1982) 223 [INSPIRE].
G.W. Gibbons and M.J. Perry, Soliton-supermultiplets and Kaluza-Klein theory, Nucl. Phys. B 248 (1984) 629 [INSPIRE].
R. Kallosh, D. Kastor, T. Ortín and T. Torma, Supersymmetry and stationary solutions in dilaton axion gravity, Phys. Rev. D 50 (1994) 6374 [hep-th/9406059] [INSPIRE].
C.M. Hull, Gravitational duality, branes and charges, Nucl. Phys. B 509 (1998) 216 [hep-th/9705162] [INSPIRE].
R. Argurio, F. Dehouck and L. Houart, Supersymmetry and gravitational duality, Phys. Rev. D 79 (2009) 125001 [arXiv:0810.4999] [INSPIRE].
R. Penrose, Naked singularities, Annals N. Y. Acad. Sci. 224 (1973) 125 [INSPIRE].
G.W. Gibbons, The isoperimetric and Bogomolny inequalities for black holes, in Global Riemannian geometry, T.J. Willmore and N. Hitchen eds., Ellis Horwood Limited, Chichester U.K. (1984), pp. 194-202 [INSPIRE].
C. LeBrun, Counter-examples to the generalized positive action conjecture, Commun. Math. Phys. 118 (1988) 591.
M.F. Atiyah and N.J. Hitchin, Low-energy scattering of non-Abelian monopoles, Phys. Lett. A 107 (1985) 21 [INSPIRE].
G.W. Gibbons and N.S. Manton, Classical and quantum dynamics of BPS monopoles, Nucl. Phys. B 274 (1986) 183 [INSPIRE].
S.A. Hayward, Inequalities relating area, energy, surface gravity and charge of black holes, Phys. Rev. Lett. 81 (1998) 4557 [gr-qc/9807003] [INSPIRE].
A.L. Yuille, Israel-Wilson metrics in the Euclidean regime, Class. Quant. Grav. 4 (1987) 1409 [INSPIRE].
B. Whitt, Israel-Wilson metrics, Annals Phys. 161 (1985) 241 [INSPIRE].
M. Dunajski and S.A. Hartnoll, Einstein-Maxwell gravitational instantons and five dimensional solitonic strings, Class. Quant. Grav. 24 (2007) 1841 [hep-th/0610261] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Gravitational multi-instantons, Phys. Lett. B 78 (1978) 430 [INSPIRE].
T. Eguchi and A.J. Hanson, Self-dual solutions to Euclidean gravity, Annals Phys. 120 (1979) 82 [INSPIRE].
C.N. Pope, Axial vector anomalies and the index theorem in charged Schwarzschild and Taub-NUT spaces, Nucl. Phys. B 141 (1978) 432 [INSPIRE].
J.P. Gauntlett and D.A. Lowe, Dyons and S duality in N = 4 supersymmetric gauge theory, Nucl. Phys. B 472 (1996) 194 [hep-th/9601085] [INSPIRE].
K.-M. Lee, E.J. Weinberg and P. Yi, Electromagnetic duality and SU(3) monopoles, Phys. Lett. B 376 (1996) 97 [hep-th/9601097] [INSPIRE].
G.W. Gibbons, The Sen conjecture for fundamental monopoles of distinct types, Phys. Lett. B 382 (1996) 53 [hep-th/9603176] [INSPIRE].
C.W. Bunster, S. Cnockaert, M. Henneaux and R. Portugues, Monopoles for gravitation and for higher spin fields, Phys. Rev. D 73 (2006) 105014 [hep-th/0601222] [INSPIRE].
G.W. Gibbons and N.P. Warner, Global structure of five-dimensional BPS fuzzballs, Class. Quant. Grav. 31 (2014) 025016 [arXiv:1305.0957] [INSPIRE].
P.H. Ginsparg and M.J. Perry, Semiclassical perdurance of de Sitter space, Nucl. Phys. B 222 (1983) 245 [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave function of the universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher spin realization of the dS/CFT correspondence, arXiv:1108.5735 [INSPIRE].
D. Anninos, F. Denef and D. Harlow, The wave function of Vasiliev’s universe: a few slices thereof, Phys. Rev. D 88 (2013) 084049 [arXiv:1207.5517] [INSPIRE].
S. Banerjee et al., Topology of future infinity in dS/CFT, JHEP 11 (2013) 026 [arXiv:1306.6629] [INSPIRE].
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Hartnoll, S.A., Ramirez, D.M. Clumping and quantum order: quantum gravitational dynamics of NUT charge. J. High Energ. Phys. 2014, 137 (2014). https://doi.org/10.1007/JHEP04(2014)137
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DOI: https://doi.org/10.1007/JHEP04(2014)137