Gaussian free field and conformal field theory

Kang, Nam-Gyu ; Makarov, Nikolai G.

Astérisque, no. 353 (2013) , 144 p.

MR Zbl

@book{AST_2013__353__R1_0,
     author = {Kang, Nam-Gyu and Makarov, Nikolai G.},
     title = {Gaussian free field and conformal field theory},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {353},
     year = {2013},
     mrnumber = {3052311},
     zbl = {1280.81004},
     language = {en},
     url = {http://www.numdam.org/item/AST_2013__353__R1_0/}
}

TY  - BOOK
AU  - Kang, Nam-Gyu
AU  - Makarov, Nikolai G.
TI  - Gaussian free field and conformal field theory
T3  - Astérisque
PY  - 2013
IS  - 353
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2013__353__R1_0/
LA  - en
ID  - AST_2013__353__R1_0
ER  -

%0 Book
%A Kang, Nam-Gyu
%A Makarov, Nikolai G.
%T Gaussian free field and conformal field theory
%S Astérisque
%D 2013
%N 353
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2013__353__R1_0/
%G en
%F AST_2013__353__R1_0

Kang, Nam-Gyu; Makarov, Nikolai G. Gaussian free field and conformal field theory. Astérisque, no. 353 (2013), 144 p. http://numdam.org/item/AST_2013__353__R1_0/

Bibliographie
Cité par

[1] Ameur (Yacin), Hedenmalm (Hâkan) & Makarov (Nikolai) - Fluctuations of eigenvalues of random normal matrices, Duke Math. J., t.159 (2011), no. 1, pp. 31-81, arXiv:0807.0375. | MR | Zbl | DOI

[2] Bauer (Michel) & Bernard (Denis) - $S L E_{κ}$ growth processes and conformal field theories, Phys. Lett. B, t. 543 (2002), no. 1-2, pp. 135-138, arXiv:math-ph/0206028. | MR | Zbl | DOI

[3] Bauer (Michel), Conformal field theories of stochastic Loewner evolutions, Comm. Math. Phys., t. 239 (2003), no. 3, pp. 493-521, arXiv:hep-th/0210015. | MR | Zbl | DOI

[4] Beffara (Vincent) - The dimension of the SLE curves, Ann. Probab., t. 36 (2008), no. 4, pp. 1421-1452, arXiv:math.PR/0211322. | MR | Zbl | DOI

[5] Belavin (A. A.), Polyakov (A. M.) & Zamolodchikov (A. B.) - Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B, t. 241 (1984), no. 2, pp. 333-380. | MR | Zbl | DOI

[6] Cardy (John L.) - Conformal invariance and surface critical behavior, Nuclear Phys. B, t. 240 (1984), pp. 514-532. | DOI

[7] Cardy (John L.), Critical percolation in finite geometries, J. Phys. A, t. 25 (1992), no. 4, pp. L201-L206, arXiv:hep-th/9111026. | MR | Zbl | DOI

[8] Cardy (John L.), SLE for theoretical physicists, Ann. Physics, t. 318 (2005), no. 1, pp. 81-118, arXiv:cond-mat/0503313. | MR | Zbl | DOI

[9] Chelkak (Dmitry) & Smirnov (Stanislav) - Universality in the $2 D$ Ising model and conformal invariance of fermionic observables, Invent. Math., t. 189 (2012), no. 3, pp. 515-580, arXiv:0910.2045. | MR | Zbl | DOI

[10] Colombeau (Jean-François) - Elementary introduction to new generalized functions, North-Holland Mathematics Studies, vol. 113, North-Holland Publishing Co., Amsterdam, 1985, Notes on Pure Mathematics, 103. | MR | Zbl

[11] Di Francesco (Philippe), Mathieu (Pierre) & Sénéchal (David) - Conformal field theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York, 1997. | MR | Zbl | DOI

[12] Dubédat (Julien) - Duality of Schramm-Loewner evolutions, Ann. Sci. Éc. Norm. Supér. (4), t. 42 (2009), no. 5, pp. 697-724, arXiv:0711.1884. | MR | Zbl | EuDML | Numdam | DOI

[13] Dubédat (Julien), SLE and the free field: partition functions and couplings, J. Amer. Math. Soc., t. 22 (2009), no. 4, pp. 995-1054, arXiv:0712.3018. | MR | Zbl | DOI

[14] Duplantier (Bertrand) - Conformally invariant fractals and potential theory, Phys. Rev. Lett., t. 84 (2000), no. 7, pp. 1363-1367, arXiv:cond-mat/9908314. | MR | Zbl | DOI

[15] Duplantier (Bertrand) & Sheffield (Scott) - Liouville quantum gravity and KPZ, Invent. Math., t. 185 (2011), no. 2, pp. 333-393, arXiv:0808.1560. | MR | Zbl | DOI

[16] Frenkel (Igor), Lepowsky (James) & Meurman (Arne) - Vertex operator algebras and the Monster, Pure and Applied Mathematics, vol. 134, Academic Press Inc., Boston, MA, 1988. | MR | Zbl

[17] Friedrich (Roland) & Werner (Wendelin) - Conformal fields, restriction properties, degenerate representations and SLE, C. R. Math. Acad. Sci. Paris, t. 335 (2002), no. 11, pp. 947-952, arXivimath/0209382. | MR | Zbl | DOI

[18] Friedrich (Roland) & Werner (Wendelin), Conformal restriction, highest-weight representations and SLE, Comm. Math. Phys., t. 243 (2003), no. 1, pp. 105-122, arXiv:math-ph/0301018. | MR | Zbl | DOI

[19] Gel'Fand (I. M.) & Fuks (D. B.) - Cohomologies of the Lie algebra of vector fields on the circle, Funkcional. Anal, i Prilozen., t. 2 (1968), no. 4, pp. 92-93. | MR | Zbl

[20] Iohara (Kenji) & Koga (Yoshiyuki) - Representation theory of the Virasoro algebra, Springer Monographs in Mathematics, Springer-Verlag London Ltd., London, 2011. | MR | Zbl | DOI

[21] Janson ( Svante) - Gaussian Hilbert spaces, Cambridge Tracts in Mathematics, vol. 129, Cambridge University Press, Cambridge, 1997. | MR | Zbl

[22] Kac (V. G.) & Raina (A. K.) - Bombay lectures on highest weight representations of infinite-dimensional Lie algebras, Advanced Series in Mathematical Physics, vol. 2, World Scientific Publishing Co. Inc., Teaneck, NJ, 1987. | MR | Zbl

[23] Kac (Victor) - Vertex algebras for beginners, second ed., University Lecture Series, vol. 10, American Mathematical Society, Providence, RI, 1998. | MR | Zbl

[24] Kang (Nam-Gyu) - Boundary behavior of SLE, J. Amer. Math. Soc, t. 20 (2007), no. 1, pp. 185-210 (electronic). | MR | Zbl

[25] Lawler (Gregory F.) - Conformally invariant processes in the plane, Mathematical Surveys and Monographs, vol. 114, American Mathematical Society, Providence, RI, 2005 | MR | Zbl

[26] Lawler (Gregory F.), Schramm-Loewner evolution (SLE), in , Statistical mechanics, IAS/Park City Math. Ser., vol. 16, Amer. Math. Soc., Providence, RI, 2009, pp. 231-295. | MR | Zbl | DOI

[27] Lawler (Gregory F.), Schramm (Oded) & Werner (Wendelin) - Values of Brownian intersection exponents. I. Half-plane exponents, Acta Math., t. 187 (2001), no. 2, pp. 237-273. | MR | Zbl | DOI

[28] Lawler (Gregory F.) Schramm (Oded Werner (Wendelin), Values of Brownian intersection exponents. II. Plane exponents, Acta Math., t. 187 (2001), no. 2, pp. 275-308. | MR | Zbl | DOI

[29] Lawler (Gregory F.) Schramm (Oded) Werner (Wendelin), Analyticity of intersection exponents for planar Brownian motion, Acta Math., t. 189 (2002), no. 2, pp. 179-201. | MR | Zbl | DOI

[30] Lawler (Gregory F.) Schramm (Oded) Werner (Wendelin), Values of Brownian intersection exponents. III. Two-sided exponents, Ann. Inst. H. Poincaré Probab. Statist., t. 38 (2002), no. 1, pp. 109-123. | MR | Zbl | EuDML | Numdam

[31] Lawler (Gregory F.) Schramm (Oded) Werner (Wendelin) , Conformal restriction: the chordal case, J. Amer. Math. Soc., t. 16 (2003), no. 4, pp. 917-955 (electronic), arXivrmath/0209343. | MR | Zbl | DOI

[32] Lawler (Gregory F.) Schramm (Oded) Werner (Wendelin), Conformal invariance of planar loop-erased random walks and uniform spanning trees, Ann. Probab., t. 32 (2004), no. 1B, pp. 939-995, arXiv:math/0112234. | MR | Zbl

[33] Lawler (Gregory F.) & Werness (Brent M.) - Multi-point Green's functions for SLE and an estimate of Beffara, (2010), Preprint, arXiv: 1011.3551. | MR | Zbl

[34] Miller (Jason) & Sheffield (Scott) - Imaginary geometry I: interacting SLEs, 2012, Preprint arXiv: 1201.1496. | MR | Zbl

[35] Revuz (Daniel) & Yor (Marc) - Continuous martingales and Brownian motion, third ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, Springer-Verlag, Berlin, 1999. | MR | Zbl | DOI

[36] Rohde (Steffen) & Schramm (Oded) - Basic properties of SLE, Ann. of Math. (2), t. 161 (2005), no. 2, pp. 883-924, arXiv:math/0106036. | MR | Zbl | DOI

[37] Rushkin (I.), Bettelheim (E.), Gruzberg (I. A.) & Wiegmann (P.) - Critical curves in conformally invariant statistical systems, J. Phys. A, t. 40 (2007), no. 9, pp. 2165-2195, arXiv:cond-mat/0610550. | MR | Zbl | DOI

[38] Schramm (Oded) - Scaling limits of loop-erased random walks and uniform spanning trees, Israel J. Math., t. 118 (2000), pp. 221-288. | MR | Zbl | DOI

[39] Schramm (Oded) & Sheffield (Scott) - A contour line of the continuum Gaussian free field, (2010), Preprint, arXiv: 1008.2447. | MR | Zbl

[40] Simon (Barry) - The $P {(ϕ)}_{2}$ Euclidean (quantum) field theory, Princeton University Press, Princeton, N.J., 1974, Princeton Series in Physics. | MR | Zbl

[41] Smirnov (Stanislav) - Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits, C. R. Acad. Sci. Paris Sér. I Math., t. 333 (2001), no. 3, pp. 239-244, arXiv:0909.4499. | MR | Zbl | DOI

[42] Smirnov (Stanislav), Towards conformal invariance of $2 D$ lattice models, in International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1421-1451. | MR | Zbl

[43] Smirnov (Stanislav), Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, Ann. of Math. (2), t. 172 (2010), no. 2, pp. 1435- 1467, arXiv:0708.0039. | MR | Zbl

[44] Werner (Wendelin) - Random planar curves and Schramm-Loewner evolutions, in Lectures on probability theory and statistics, Lecture Notes in Math., vol. 1840, Springer, Berlin, 2004, pp. 107-195. | MR | Zbl

[45] Werner (Wendelin), Lectures on two-dimensional critical percolation, in Statistical mechanics, IAS/Park City Math. Ser., vol. 16, Amer. Math. Soc., Providence, RI, 2009, pp. 297-360. | MR | Zbl | DOI

[46] Zhan (Dapeng) - Duality of chordal SLE, Invent. Math., t. 174 (2008), no. 2, pp. 309-353, arXiv:0712.0332. | MR | Zbl | DOI