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Quantum Gravity as a Fermi Liquid

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Abstract

We present a reformulation of loop quantum gravity with a cosmological constant and no matter as a Fermi-liquid theory. When the topological sector is deformed and large gauge symmetry is broken, we show that the Chern–Simons state reduces to Jacobson’s degenerate sector describing 1+1 dimensional propagating fermions with nonlocal interactions. The Hamiltonian admits a dual description which we realize in the simple BCS model of superconductivity. On one hand, Cooper pairs are interpreted as wormhole correlations at the de Sitter horizon; their number yields the de Sitter entropy. On the other hand, BCS is mapped into a deformed conformal field theory reproducing the structure of quantum spin networks. When area measurements are performed, Cooper-pair insertions are activated on those edges of the spin network intersecting the given area, thus providing a description of quantum measurements in terms of excitations of a Fermi sea to superconducting levels. The cosmological constant problem is naturally addressed as a nonperturbative mass-gap effect of the true Fermi-liquid vacuum.

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References

  1. Rovelli, C.: Living Rev. Relativ. 1, 1 (1998). gr-qc/9710008

    ADS  MathSciNet  Google Scholar 

  2. Thiemann, T.: Lect. Not. Phys. 631, 412003 (2003). gr-qc/0210094

    MathSciNet  Google Scholar 

  3. Smolin, L.: hep-th/0408048 (2004)

  4. Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  5. Ashtekar, A., Corichi, A., Singh, P.: Phys. Rev. D, 77, 024046 (2008). 0710.3565 [gr-qc]

    ADS  MathSciNet  Google Scholar 

  6. Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  7. Ashtekar, A.: Phys. Rev. Lett. 57, 2244 (1986)

    ADS  MathSciNet  Google Scholar 

  8. Perez, A., Rovelli, C.: Phys. Rev. D 73, 044013 (2006). gr-qc/0505081

    ADS  MathSciNet  Google Scholar 

  9. Alexander, S., Vaid, D.: hep-th/0609066 (2006)

  10. Alexander, S., Vaid, D.: hep-th/0702064 (2007)

  11. Alexander, S.H.S., Calcagni, G.: 0806.4382 [hep-th] (2008)

  12. Samuel, J.: Pramana 28, L429 (1987)

    ADS  Google Scholar 

  13. Mena Marugán, G.A.: Int. J. Mod. Phys. D 3, 513 (1994). gr-qc/9311020

    ADS  Google Scholar 

  14. Smolin, L.: hep-th/0209079 (2002)

  15. Montesinos, M.: Class. Quantum Gravity 18, 1847 (2001). gr-qc/0104068

    MATH  ADS  MathSciNet  Google Scholar 

  16. Brügmann, B., Gambini, R., Pullin, J.: Phys. Rev. Lett. 68, 431 (1992)

    MATH  ADS  MathSciNet  Google Scholar 

  17. Treiman, S.B., Jackiw, R., Zumino, B., Witten, E.: Current Algebra and Anomalies. World Scientific, Singapore (1985)

    MATH  Google Scholar 

  18. Kodama, H.: Prog. Theor. Phys. 80, 1024 (1988)

    ADS  MathSciNet  Google Scholar 

  19. Kodama, H.: Phys. Rev. D 42, 2548 (1990)

    ADS  MathSciNet  Google Scholar 

  20. Chern, S.S., Simons, J.: Ann. Math. 99, 48 (1974)

    MathSciNet  Google Scholar 

  21. Soo, C.: Class. Quantum Gravity 19, 1051 (2002). gr-qc/0109046

    MATH  ADS  MathSciNet  Google Scholar 

  22. Gambini, R., Pullin, J.: Loops, Knots, Gauge Theories and Quantum Gravity. Cambridge University Press, Cambridge (1996)

    MATH  Google Scholar 

  23. Gambini, R., Obregon, O., Pullin, J.: Phys. Rev. D 59, 047505 (1999). gr-qc/9801055

    ADS  MathSciNet  Google Scholar 

  24. Mercuri, S.: Phys. Rev. D 77, 024036 (2008). 0708.0037 [gr-qc]

    ADS  MathSciNet  Google Scholar 

  25. Callan, C.G., Dashen, R.F., Gross, D.J.: Phys. Lett. B 63, 334 (1976)

    ADS  Google Scholar 

  26. Jackiw, R., Rebbi, C.: Phys. Rev. Lett. 37, 172 (1976)

    ADS  Google Scholar 

  27. Weinberg, S.: The Quantum Theory of Fields, vol. II. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  28. Deser, S., Duff, M.J., Isham, C.J.: Phys. Lett. B 93, 419 (1980)

    ADS  Google Scholar 

  29. Ashtekar, A., Balachandran, A.P., Jo, S.: Int. J. Mod. Phys. A 4, 1493 (1989)

    ADS  MathSciNet  Google Scholar 

  30. Paternoga, R., Graham, R.: Phys. Rev. D 62, 084005 (2000). gr-qc/0003111

    ADS  MathSciNet  Google Scholar 

  31. Smolin, L., Soo, C.: Nucl. Phys. B 449, 289 (1995). gr-qc/9405015

    MATH  ADS  MathSciNet  Google Scholar 

  32. Jacobson, T., Smolin, L.: Nucl. Phys. B 299, 295 (1988)

    ADS  MathSciNet  Google Scholar 

  33. Gambini, R., Trias, A.: Nucl. Phys. B 278, 436 (1986)

    ADS  MathSciNet  Google Scholar 

  34. Rovelli, C., Smolin, L.: Phys. Rev. Lett. 61, 1155 (1988)

    ADS  MathSciNet  Google Scholar 

  35. Rovelli, C., Smolin, L.: Nucl. Phys. B 331, 80 (1990)

    ADS  MathSciNet  Google Scholar 

  36. Brügmann, B., Gambini, R., Pullin, J.: Nucl. Phys. B 385, 587 (1992). hep-th/9202018

    ADS  Google Scholar 

  37. Brügmann, B., Gambini, R., Pullin, J.: Gen. Relativ. Gravit. 25, 1 (1993). hep-th/9203040

    MATH  ADS  Google Scholar 

  38. Witten, E.: Commun. Math. Phys. 121, 351 (1989)

    MATH  ADS  MathSciNet  Google Scholar 

  39. Kauffman, L.H.: Knots and Physics. Series on Knots and Everything, vol. 1. World Scientific, Singapore (1991)

    MATH  Google Scholar 

  40. Kauffman, L.H., Lins, S.L.: Temperley–Lieb Recoupling Theory and Invariants of 3-Manifolds. Princeton University Press, Princeton (1994)

    MATH  Google Scholar 

  41. Baez, J., Muniain, J.P.: Gauge Fields, Knots and Gravity. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  42. Kauffman, L.H., Lomonaco, S.J.: 0707.3678 [quant-ph] (2007)

  43. Witten, E.: gr-qc/0306083 (2003)

  44. Randono, A.: gr-qc/0611073 (2006)

  45. Randono, A.: gr-qc/0611074 (2006)

  46. Randono, A.: 0805.2955 [gr-qc] (2008)

  47. Adler, S.L.: Phys. Rev. 177, 2426 (1969)

    ADS  Google Scholar 

  48. Bell, J.S., Jackiw, R.: Nuovo Cim. A 60, 47 (1969)

    ADS  Google Scholar 

  49. ’t Hooft, G.: Phys. Rev. Lett. 37, 8 (1976)

    ADS  Google Scholar 

  50. ’t Hooft, G.: Phys. Rev. D 14, 3432 (1976). Erratum-ibid. D 18, 2199 (1978)

    ADS  Google Scholar 

  51. Peccei, R.D., Quinn, H.R.: Phys. Rev. Lett. 38, 1440 (1977)

    ADS  Google Scholar 

  52. Peccei, R.D., Quinn, H.R.: Phys. Rev. D 16, 1791 (1977)

    ADS  Google Scholar 

  53. Cooper, F., Venturi, G.: Phys. Rev. D 24, 3338 (1981)

    ADS  MathSciNet  Google Scholar 

  54. Bojowald, M., Hossain, G.M., Kagan, M., Shankaranarayanan, S.: 0806.3929 [gr-qc] (2008)

  55. Jacobson, T.: Class. Quantum Gravity 13, L111 (1996). Erratum-ibid. 13, 3269 (1996). gr-qc/9604003

    ADS  Google Scholar 

  56. Horowitz, G.T.: hep-th/9109030 (1991)

  57. Horowitz, G.T.: Class. Quantum Gravity 8, 587 (1991)

    MATH  ADS  MathSciNet  Google Scholar 

  58. Matschull, H.J.: Class. Quantum Gravity 13, 765 (1996). gr-qc/9511034

    MATH  ADS  MathSciNet  Google Scholar 

  59. Lewandowski, J., Wiśniewski, J.: Class. Quantum Gravity 14, 775 (1997). gr-qc/9609019

    MATH  ADS  Google Scholar 

  60. Lewandowski, J., Wiśniewski, J.: Class. Quantum Gravity 16, 3057 (1999). gr-qc/9902037

    MATH  ADS  Google Scholar 

  61. Ashtekar, A., Romano, J.D., Tate, R.S.: Phys. Rev. D 40, 2572 (1989)

    ADS  MathSciNet  Google Scholar 

  62. Volovik, G.E.: Proc. Natl. Acad. Sci. 96, 6042 (1999). cond-mat/9812381

    ADS  Google Scholar 

  63. Volovik, G.E.: Phys. Rep. 351, 195 (2001). gr-qc/0005091

    MATH  ADS  MathSciNet  Google Scholar 

  64. Volovik, G.E.: The Universe in a Helium Droplet. Clarendon Press, Oxford (2003)

    MATH  Google Scholar 

  65. Volovik, G.E.: J. Low Temp. Phys. 24, 127 (1998). cond-mat/9706172

    Google Scholar 

  66. Volovik, G.E.: JETP Lett. 67, 698 (1998). cond-mat/9804078

    ADS  Google Scholar 

  67. Volovik, G.E.: J. Low Temp. Phys. 113, 667 (1997). cond-mat/9806010

    Google Scholar 

  68. Volovik, G.E.: Gravit. Cosmol. Suppl. 6, 187 (2000). gr-qc/0004049

    MathSciNet  Google Scholar 

  69. Volovik, G.E.: gr-qc/0101111 (2001)

  70. Volovik, G.E.: JETP Lett. 82, 319 (2005). gr-qc/0505104

    ADS  Google Scholar 

  71. Volovik, G.E.: Int. J. Mod. Phys. D 15, 1987 (2006). gr-qc/0604062

    MATH  ADS  MathSciNet  Google Scholar 

  72. Jacobson, T.A., Volovik, G.E.: Phys. Rev. D 58, 064021 (1998)

    ADS  Google Scholar 

  73. Jacobson, T.A., Volovik, G.E.: JETP Lett. 68, 874 (1998). gr-qc/9811014

    ADS  Google Scholar 

  74. Volovik, G.E.: JETP Lett. 70, 711 (1999). gr-qc/9911026

    ADS  Google Scholar 

  75. Fischer, U.R., Volovik, G.E.: Int. J. Mod. Phys. D 10, 57 (2001). gr-qc/0003017

    ADS  Google Scholar 

  76. Volovik, G.E.: Found. Phys. 33, 349 (2003). gr-qc/0301043

    MathSciNet  Google Scholar 

  77. Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175 (1957)

    MATH  ADS  MathSciNet  Google Scholar 

  78. Bogoliubov, N.N.: Nuovo Cim. 7, 794 (1958)

    Google Scholar 

  79. Morales-Técotl, H.A., Rovelli, C.: Phys. Rev. Lett. 72, 3642 (1994)

    MATH  ADS  MathSciNet  Google Scholar 

  80. Morales-Técotl, H.A., Rovelli, C.: Nucl. Phys. B 451, 325 (1995). gr-qc/9401011

    MATH  ADS  Google Scholar 

  81. Sierra, G.: Nucl. Phys. B 572, 517 (2000). hep-th/9911078

    MATH  ADS  MathSciNet  Google Scholar 

  82. Asorey, M., Falceto, F., Sierra, G.: Nucl. Phys. B 622, 593 (2002). hep-th/0110266

    MATH  ADS  MathSciNet  Google Scholar 

  83. Sierra, G.: hep-th/0111114 (2001)

  84. Mahan, G.D.: Many-Particle Physics. Kluwer/Plenum, New York (2000)

    Google Scholar 

  85. Richardson, R.W.: Phys. Lett. 3, 277 (1963)

    MATH  ADS  Google Scholar 

  86. Richardson, R.W., Sherman, N.: Nucl. Phys. B 52, 221 (1964)

    MathSciNet  Google Scholar 

  87. von Delft, J., Braun, F.: cond-mat/9911058 (1999)

  88. Crane, L.: Commun. Math. Phys. 135, 615 (1991)

    MATH  ADS  MathSciNet  Google Scholar 

  89. Crane, L.: Phys. Lett. B 259, 243 (1991)

    ADS  MathSciNet  Google Scholar 

  90. Markopoulou, F., Smolin, L.: Phys. Rev. D 58, 084032 (1998). gr-qc/9712067

    ADS  MathSciNet  Google Scholar 

  91. Kauffman, L.H., Lomonaco, S.J.: quant-ph/0606114 (2006)

  92. Penrose, R.: In: Bastin, T. (ed.) Quantum Theory and Beyond. Cambridge University Press, Cambridge (1971)

    Google Scholar 

  93. Moussouris, J.: Quantum models of space-time based on recoupling theory. Ph.D. thesis, Oxford (1983)

  94. Rovelli, C., Smolin, L.: Phys. Rev. D 52, 5743 (1995). gr-qc/9505006

    ADS  MathSciNet  Google Scholar 

  95. Wess, J., Zumino, B.: Phys. Lett. B 37, 95 (1971)

    ADS  MathSciNet  Google Scholar 

  96. Witten, E.: Commun. Math. Phys. 92, 455 (1984)

    MATH  ADS  MathSciNet  Google Scholar 

  97. Polchinski, J.: String Theory. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  98. Kac, V.: Infinite Dimensional Lie Algebras. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  99. Kac, V.G., Kazhdan, D.A.: Adv. Math. 34, 97 (1979)

    MATH  MathSciNet  Google Scholar 

  100. Wakimoto, M.: Commun. Math. Phys. 104, 605 (1986)

    MATH  ADS  MathSciNet  Google Scholar 

  101. Gerasimov, A., Morozov, A., Olshanetsky, M., Marshakov, A., Shatashvili, S.L.: Int. J. Mod. Phys. A 5, 2495 (1990)

    ADS  MathSciNet  Google Scholar 

  102. Dotsenko, V.S., Fateev, V.A.: Nucl. Phys. B 240, 312 (1984)

    ADS  MathSciNet  Google Scholar 

  103. Dotsenko, V.S., Fateev, V.A.: Nucl. Phys. B 251, 691 (1985)

    ADS  MathSciNet  Google Scholar 

  104. Dotsenko, V.S.: Nucl. Phys. B 338, 747 (1990)

    ADS  MathSciNet  Google Scholar 

  105. Dotsenko, V.S.: Nucl. Phys. B 358, 547 (1991)

    ADS  MathSciNet  Google Scholar 

  106. Knizhnik, V.G., Zamolodchikov, A.B.: Nucl. Phys. B 247, 83 (1984)

    MATH  ADS  MathSciNet  Google Scholar 

  107. Moore, G., Seiberg, N.: Phys. Lett. B 220, 422 (1989)

    ADS  MathSciNet  Google Scholar 

  108. Elitzur, S., Moore, G., Schwimmer, A., Seiberg, N.: Nucl. Phys. B 326, 108 (1989)

    ADS  MathSciNet  Google Scholar 

  109. Feigin, B., Frenkel, E.: Int. J. Mod. Phys. A 7S1A, 197 (1992)

    MathSciNet  Google Scholar 

  110. Bakas, I., Kiritsis, E.: Int. J. Mod. Phys. A 7S1A, 55 (1992). hep-th/9109029

    MathSciNet  Google Scholar 

  111. Bakas, I., Sourdis, C.: J. High Energy Phys. 0406, 049 (2004). hep-th/0403165

    ADS  MathSciNet  Google Scholar 

  112. Bakas, I., Sourdis, C.: Fortsch. Phys. 53, 409 (2005). hep-th/0501127

    MathSciNet  Google Scholar 

  113. Bouwknegt, P., Schoutens, K.: Phys. Rep. 223, 183 (1993). hep-th/9210010

    ADS  MathSciNet  Google Scholar 

  114. Witten, E.: Phys. Rev. D 44, 314 (1991)

    ADS  MathSciNet  Google Scholar 

  115. Kazakov, V., Kostov, I.K., Kutasov, D.: Nucl. Phys. B 622, 141 (2002). hep-th/0101011

    MATH  ADS  MathSciNet  Google Scholar 

  116. Pope, C., Romans, L.J., Shen, X.: Phys. Lett. B 236, 173 (1990)

    ADS  MathSciNet  Google Scholar 

  117. Pope, C., Romans, L.J., Shen, X.: Nucl. Phys. B 339, 191 (1990)

    ADS  MathSciNet  Google Scholar 

  118. Park, Q.H.: Phys. Lett. B 236, 429 (1990)

    ADS  MathSciNet  Google Scholar 

  119. Park, Q.H.: Phys. Lett. B 238, 287 (1990)

    ADS  MathSciNet  Google Scholar 

  120. Husain, V.: Class. Quantum Gravity 10, 543 (1993). hep-th/9206058

    MATH  ADS  MathSciNet  Google Scholar 

  121. Cambiaggio, M.C., Rivas, A.M.F., Saraceno, M.: Nucl. Phys. A 624, 157 (1997). nucl-th/9708031

    ADS  Google Scholar 

  122. Doniach, S., Inui, M.: Phys. Rev. B 41, 6668 (1990)

    ADS  Google Scholar 

  123. Emery, V.J., Kivelson, S.A.: Nature 374, 434 (1995)

    ADS  Google Scholar 

  124. Emery, V.J., Kivelson, S.A.: Phys. Rev. Lett. 74, 3253 (1995)

    ADS  Google Scholar 

  125. Freidel, L.: 0804.0632 [hep-th] (2008)

  126. Kamimura, K., Makita, S., Fukuyama, T.: Mod. Phys. Lett. A 6, 3047 (1991)

    MATH  ADS  MathSciNet  Google Scholar 

  127. Bekenstein, J.D.: Phys. Rev. D 7, 2333 (1973)

    ADS  MathSciNet  Google Scholar 

  128. Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975)

    ADS  MathSciNet  Google Scholar 

  129. Spradlin, M., Strominger, A., Volovich, A.: hep-th/0110007 (2001)

  130. Bousso, R.: Rev. Mod. Phys. 74, 825 (2002). hep-th/0203101

    ADS  MathSciNet  Google Scholar 

  131. Bojowald, M.: Living Rev. Relativ. 8, 11 (2005). gr-qc/0601085

    ADS  Google Scholar 

  132. Bojowald, M.: Int. J. Mod. Phys. D 15, 1545 (2006). gr-qc/0607130

    MATH  ADS  MathSciNet  Google Scholar 

  133. Ashtekar, A.: 0810.0514 [gr-qc] (2008)

  134. Friedman, J.L., Sorkin, R.D.: Phys. Rev. Lett. 44, 1100 (1980)

    ADS  Google Scholar 

  135. Friedman, J.L., Sorkin, R.D.: Gen. Relativ. Gravit. 14, 615 (1982)

    ADS  MathSciNet  Google Scholar 

  136. Samuel, J.: Phys. Rev. Lett. 71, 215 (1993)

    MATH  ADS  MathSciNet  Google Scholar 

  137. Hansson, T.H., Chang, C.C., Jain, J.K., Viefers, S.: Phys. Rev. Lett. 98, 076801 (2007). cond-mat/0603125

    ADS  Google Scholar 

  138. de Vega, H.J., Sanchez, N.G.: Phys. Lett. B 197, 320 (1987)

    ADS  MathSciNet  Google Scholar 

  139. De Vega, H.J., Nicolaidis, A.: Phys. Lett. B 295, 214 (1992)

    ADS  Google Scholar 

  140. de Vega, H.J., Giannakis, I., Nicolaidis, A.: Mod. Phys. Lett. A 10, 2479 (1995). hep-th/9412081

    Article  MATH  ADS  Google Scholar 

  141. Schild, A.: Phys. Rev. D 16, 1722 (1977)

    ADS  Google Scholar 

  142. Karlhede, A., Lindström, U.: Class. Quantum Gravity 3, L73 (1986)

    ADS  Google Scholar 

  143. Gross, D.J., Mende, P.F.: Phys. Lett. B 197, 129 (1987)

    ADS  MathSciNet  Google Scholar 

  144. Gross, D.J., Mende, P.F.: Nucl. Phys. B 303, 407 (1988)

    ADS  MathSciNet  Google Scholar 

  145. Gross, D.J.: Phys. Rev. Lett. 60, 1229 (1988)

    ADS  MathSciNet  Google Scholar 

  146. Lindström, U., Zabzine, M.: Phys. Lett. B 584, 178 (2004). hep-th/0305098

    ADS  MathSciNet  Google Scholar 

  147. Savvidy, G.K.: Int. J. Mod. Phys. A 19, 3171 (2004). hep-th/0310085

    MATH  ADS  MathSciNet  Google Scholar 

  148. Savvidy, G.K.: Phys. Lett. B 615, 285 (2005). hep-th/0502114

    ADS  MathSciNet  Google Scholar 

  149. Lizzi, F., Rai, B., Sparano, G., Srivastava, A.: Phys. Lett. B 182, 326 (1986)

    ADS  MathSciNet  Google Scholar 

  150. Fradkin, E.S., Vasiliev, M.A.: Phys. Lett. B 189, 89 (1987)

    MATH  ADS  MathSciNet  Google Scholar 

  151. Blencowe, M.P.: Class. Quantum Gravity 6, 443 (1989)

    ADS  MathSciNet  Google Scholar 

  152. Engquist, J., Hohm, O.: Nucl. Phys. B 786, 1 (2007). 0705.3714 [hep-th]

    MATH  ADS  MathSciNet  Google Scholar 

  153. Brandenberger, R.H., Vafa, C.: Nucl. Phys. B 316, 391 (1989)

    ADS  MathSciNet  Google Scholar 

  154. Sakagami, M.: Prog. Theor. Phys. 79, 442 (1988)

    ADS  Google Scholar 

  155. Halliwell, J.J.: Phys. Rev. D 39, 2912 (1989)

    ADS  MathSciNet  Google Scholar 

  156. Padmanabhan, T.: Phys. Rev. D 39, 2924 (1989)

    ADS  Google Scholar 

  157. Kiefer, C.: Phys. Rev. D 47, 5414 (1993). gr-qc/9306016

    ADS  MathSciNet  Google Scholar 

  158. Ashtekar, A., Schilling, T.A.: gr-qc/9706069 (1997)

  159. Zurek, W.H.: Rev. Mod. Phys. 75, 715 (2003)

    ADS  MathSciNet  Google Scholar 

  160. Lauscher, O., Reuter, M.: Phys. Rev. D 65, 025013 (2002). hep-th/0108040

    ADS  MathSciNet  Google Scholar 

  161. Lauscher, O., Reuter, M.: J. High Energy Phys. 0510, 050 (2005). hep-th/0508202

    ADS  MathSciNet  Google Scholar 

  162. Niedermaier, M., Reuter, M.: Living Rev. Relativ. 9, 5 (2006). [Online article: http://www.livingreviews.org/lrr-2006-5]

    ADS  Google Scholar 

  163. Ambjørn, J., Jurkiewicz, J.: Phys. Lett. B 278, 42 (1992)

    ADS  MathSciNet  Google Scholar 

  164. Agishtein, M.E., Migdal, A.A.: Nucl. Phys. B 385, 395 (1992). hep-lat/9204004

    ADS  MathSciNet  Google Scholar 

  165. Ambjørn, J., Loll, R.: Nucl. Phys. B 536, 407 (1998). hep-th/9805108

    ADS  Google Scholar 

  166. Ambjørn, J., Jurkiewicz, J., Loll, R.: Phys. Rev. Lett. 85, 924 (2000). hep-th/0002050

    ADS  MathSciNet  Google Scholar 

  167. Ambjørn, J., Jurkiewicz, J., Loll, R.: Nucl. Phys. B 610, 347 (2001). hep-th/0105267

    ADS  Google Scholar 

  168. Ambjørn, J., Jurkiewicz, J., Loll, R.: Phys. Rev. Lett. 93, 131301 (2004). hep-th/0404156

    ADS  MathSciNet  Google Scholar 

  169. Ambjørn, J., Jurkiewicz, J., Loll, R.: Phys. Rev. Lett. 95, 171301 (2005). hep-th/0505113

    ADS  Google Scholar 

  170. Ambjørn, J., Jurkiewicz, J., Loll, R.: Phys. Rev. D 72, 064014 (2005). hep-th/0505154

    ADS  Google Scholar 

  171. Ambjørn, J., Jurkiewicz, J., Loll, R.: Contemp. Phys. 47, 103 (2006). hep-th/0509010

    ADS  Google Scholar 

  172. Ambjørn, J., Görlich, A., Jurkiewicz, J., Loll, R.: Phys. Rev. Lett. 100, 091304 (2008). 0712.2485 [hep-th]

    ADS  Google Scholar 

  173. Loll, R.: Class. Quantum Gravity 25, 114006 (2008). 0711.0273 [gr-qc]

    ADS  MathSciNet  Google Scholar 

  174. Horava, P., Keeler, C.A.: J. High Energy Phys. 0707, 059 (2007). hep-th/0508024

    ADS  MathSciNet  Google Scholar 

  175. Hartnoll, S.A., Herzog, C.P., Horowitz, G.T.: 0803.3295 [hep-th] (2008)

  176. Bilson-Thompson, S.O., Markopoulou, F., Smolin, L.: Class. Quantum Gravity 24, 3975 (2007). hep-th/0603022

    MATH  ADS  MathSciNet  Google Scholar 

  177. Bilson-Thompson, S., Hackett, J., Kauffman, L., Smolin, L.: 0804.0037 [hep-th] (2008)

  178. Fustero, X., Gambini, R., Trias, A.: Phys. Rev. Lett. 62, 1964 (1989)

    ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute for Gravitation and the Cosmos, Department of Physics, The Pennsylvania State University, 104 Davey Lab, University Park, PA, 16802, USA

    Stephon H. S. Alexander & Gianluca Calcagni

  2. Department of Physics, Haverford College, 370 Lancaster Avenue, Haverford, PA, 19041, USA

    Stephon H. S. Alexander

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  1. Stephon H. S. Alexander
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  2. Gianluca Calcagni
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Correspondence to Gianluca Calcagni.

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Alexander, S.H.S., Calcagni, G. Quantum Gravity as a Fermi Liquid. Found Phys 38, 1148–1184 (2008). https://doi.org/10.1007/s10701-008-9257-6

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  • DOI: https://doi.org/10.1007/s10701-008-9257-6

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