Geodesic
Massive Majorana fermion coupled to two-dimensional gravity and the
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 3, pp. 372-398
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We consider the partition function of the two-dimensional free massive Majorana fermion coupled to the quantized metric of the spherical topology. By adding an arbitrary conformal “spectator” matter, we gain control over the total matter central charge. This provides an interesting continuously parameterized family of critical points and also allows making a connection with the semiclassical limit. We use the Liouville field theory as the effective description of the quantized gravity. The spherical scaling function is calculated approximately, but {(}we believe{\rm)} to a good numerical precision, in almost the whole domain of the spectator parameter. An impressive comparison with the predictions of the exactly solvable matrix model yields a more general model of random-lattice statistics, which is most probably not solvable by the matrix-model technique but reveals a more general pattern of critical behavior. We hope that numerical simulations or series extrapolation will be able to reveal our family of scaling functions.
Keywords: Liouville field theory, two-dimensional gravity, Ising model, random lattice. 
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Al. B. Zamolodchikov; Yu. Ishimoto. Massive Majorana fermion coupled to two-dimensional gravity and the. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 3, pp. 372-398. http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a1/

[1] Al. Zamolodchikov, “Perturbed conformal field theory on fluctuating sphere. Contribution to the Balkan Workshop BW2003”, Mathematical, Theoretical and Phenomenological Challenges Beyond Standard Model (29 August – 02 September 2003, Vrnjancka Banja, Serbia)

[2] V. A. Kazakov, Phys. Lett. B, 150 (1985), 282 | DOI | MR

[3] F. David, Nucl. Phys. B, 257 (1985), 543 | DOI | MR

[4] V. Kazakov, I. Kostov, A. Migdal, Phys. Lett. B, 157 (1985), 295 | DOI | MR

[5] D. Boulatov, V. Kazakov, I. Kostov, A. Migdal, Nucl. Phys. B, 275 (1986), 641 | DOI | MR | Zbl

[6] A. Polyakov, Phys. Lett. B, 103 (1981), 207 | DOI | MR

[7] T. Regge, Phys. Rev., 108 (1961), 558

[8] V. Knizhnik, A. Polyakov, A. Zamolodchikov, Mod. Phys. Lett. A, 3 (1988), 819 | DOI | MR

[9] F. David, Mod. Phys. Lett. A, 3 (1988), 1651 ; J. Distler, H. Kawai, Nucl. Phys. B, 231 (1989), 509 | DOI | MR | DOI | MR

[10] M. Goulian, M. Li, Phys. Rev. Lett., 66 (1991), 2051 ; V. S. Dotsenko, Mod. Phys. Lett. A, 6 (1991), 3601 ; “Correlation functions of local operators in 2-D gravity coupled to minimal matter”, New Symmetry Principles in Quantum Field Theory, Proc. Adv. Study Inst. (Cargese, France, 1991), NATO Sci. Ser. B, 295, eds. J. Fröhlich, G. 't Hooft, A. Joffe et al., Plenum, NY, 1992, 432 ; hep-th/9110030 | DOI | DOI | MR | Zbl | MR

[11] H. Dorn, H.-J. Otto, Phys. Lett. B, 291 (1992), 39 ; ; Nucl. Phys. B, 429 (1994), 375 ; hep-th/9206053hep-th/9403141 | DOI | MR | DOI | MR | Zbl

[12] A. Zamolodchikov, Al. Zamolodchikov, Nucl. Phys. B, 477 (1996), 577 | DOI | MR | Zbl

[13] J. Teschner, Phys. Lett. B, 363 (1995), 65 ; hep-th/9507109 | DOI

[14] V. Fateev, A. Zamolodchikov, Al. Zamolodchikov, Boundary Liouville field theory. I: Boundary state and boundary two-point function, hep-th/0001012 | MR

[15] E. Brézin, C. Itzykson, G. Parisi, J.-B. Zuber, Commun. Math. Phys., 59 (1978), 35 | DOI | MR | Zbl

[16] V. Kazakov, Pisma v ZhETF, 44 (1986), 105 | MR

[17] D. Boulatov, V. Kazakov, Phys. Lett. B, 186 (1987), 379 | DOI | MR

[18] P. Di Francesco, D. Kutasov, Phys. Lett. B, 261 (1991), 385 | DOI | MR

[19] Y. Ishimoto, S. Yamaguchi, Phys. Lett. B, 607 (2005), 172 ; ; Ал. Замолодчиков, ТМФ, 142:2 (2005), 218 ; ; А. А. Белавин, Ал. Б. Замолодчиков, ТМФ, 147:3 (2006), 339 hep-th/0406262hep-th/0505063 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[20] Al. Zamolodchikov, JHEP, 0207 (2002), 029 ; hep-th/0109078 | DOI | MR

[21] F. David, Nucl. Phys. B, 257 (1985), 543 | DOI | MR

[22] D. Boulatov, V. Kazakov, I. Kostov, A. Migdal, Bulg. J. Phys., 13 (1986), 313 | MR

[23] P. Ginsparg, G. Moore, “Lectures on 2-D gravity and 2-D string theory”, TASI summer school (June 11–19, Boulder CO, 1992, USA)

[24] Z. Burda, J. Jurkiewicz, The Ising model on a random lattice with a coordination number equal 3, Kraków University Preprint TPJU-1/89, 1989 | MR

[25] Al. Zamolodchikov, Commun. Math. Phys., 96 (1984), 419 ; Ал. Б. Замолодчиков, ТМФ, 73:1 (1987), 103 | DOI | MR | MR

[26] Al. Zamolodchikov, Gravitational Yang–Lee model. Four point function, In preparation