algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
A 2d CFT is called logarithmic (LCFT) if it looks like a rational conformal field theory except that some of the 2-point functions may have a logarithmic dependence on the field insertion, in addition to the usual power law (see, e.g. Fuchs & Schweigert 2019, (8) for a clear account).
A classical example of a logarithmic CFT it the “triple algebra of the Virasoso model”, see the references below.
More recently it was understood (Gaberdiel 2001, review in Ridout 2010, 2020) that the chiral WZW models at “admissible” fractional levels are examples of logarithmic CFTs, see the references further below. (The WZW model at non-integer-level does not have a geometric sigma-model-description but but it still does make sense as a current algebra/vertex operator algebra/modular functor of conformal blocks).
In fact, the triple algebra -model turns out to be essentially equivalent to the -WZW model at admissible level (Nichols 2002, cf. at KZ-equation, here).
Original articles:
Review:
Matthias R. Gaberdiel, An algebraic approach to logarithmic conformal field theory, Int. J. Mod. Phys. A 18 (2003) 4593-4638 arXiv:hep-th/0111260, doi:10.1142/S0217751X03016860
Michael Flohr, Bits and pieces in logarithmic conformal field theory, International Journal of Modern Physics A, 18 25 (2003) 4497-4591 doi:10.1142/S0217751X03016859, arXiv:hep-th/0111228
Thomas Creutzig, David Ridout, Logarithmic conformal field theory: beyond an introduction, J. Phys. A: Math. Theor. 46 (2013) 494006 (doi:10.1088/1751-8113/46/49/494006, arXiv:1303.0847)
Matthijs Hogervorst, Miguel Paulos, Alessandro Vichi, The ABC (in any D) of logarithmic CFT, J. High Energ. Phys. 2017 201 (2017) doi:10.1007/JHEP10(2017)201201), arXiv:1605.03959
On the Verlinde formula for logarithmic CFTs:
David Ridout, Simon Wood, The Verlinde formula in logarithmic CFT, J. Phys.: Conf. Ser. 597 012065 arXiv:1409.0670, doi:10.1088/1742-6596/597/1/012065
Thomas Creutzig, Terry Gannon, Logarithmic conformal field theory, log-modular tensor categories and modular forms, J. Phys. A 50, 404004 (2017) (doi:10.1088/1751-8121/aa8538, arXiv:1605.04630)
On the braided tensor categories corresponding to logarithmic CFTs:
On generalizing the FRS-theorem on rational 2d CFT to logarithmic 2dCFTs:
Logarithmic CFT describing generalized Laughlin wavefunctions with topological order:
Victor Gurarie, Michael Flohr, Chetan Nayak, The Haldane-Rezayi Quantum Hall State and Conformal Field Theory, Nucl. Phys. B 498 (1997) 513-538 arXiv:cond-mat/9701212, doi:10.1016/S0550-3213%2897%2900351-9
(review in Flohr 2003, §5.4)
See also:
D. Adamović, A. Milas, Lattice construction of logarithmic modules for certain vertex algebras, Selecta Math. New Ser. 15 (2009), 535–561 arxiv/0902.3417; An analogue of modular BPZ equation in logarithmic (super)conformal field theory, to appear in Contemporary Mathematics 497; An explicit realization of logarithmic modules for the vertex operator algebra , arxiv/1202.6667; -cofinite W-algebras and their logarithmic representations_, arxiv/1212.6771; Logarithmic intertwining operators and -algebras, J.Math.Phys.48:073503, 2007, arxiv/math.RT/0702081
2011 workshop Logarithmic CFT and representation theory
Matthias R Gaberdiel, Ingo Runkel, From boundary to bulk in logarithmic CFT, J. Phys. A: Math. Theor. 41 075402 (2008) doi
A. M. Semikhatov, I. Yu. Tipunin, Logarithmic CFT models from Nichols algebras 1, arxiv/1301.2235
A. M. Semikhatov, Factorizable ribbon quantum groups in logarithmic conformal field theories, Theor.Math.Phys.154:433-453, 2008 arxiv/0705.4267; A Heisenberg double addition to the logarithmic Kazhdan–Lusztig duality, Lett.Math.Phys.92:81-98, 2010 arxiv/0905.2215
Boris Feigin, A M Gainutdinov, A M Semikhatov, I Yu Tipunin, Logarithmic extensions of minimal models: characters and modular transformations, Nucl.Phys. B757:303-343,2006 hep-th/0606196;
and in the quantum group center_, Commun. Math. Phys. 265 (2006) 47–93;
Kazhdan–Lusztig correspondence for the representation category of the triplet -algebra in logarithmic CFT, Theor. Math. Phys. 148 (2006) 1210–1235;
Kazhdan–Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models, J. Math. Phys. 48 (2007) 032303
Philippe Ruelle, Logarithmic conformal invariance in the Abelian sandpile model, arxiv/1303.4310
Victor Gurarie, Logarithmic Operators in Conformal Field Theory, Nucl.Phys. B 410 (1993) 535-549 arXiv:hep-th/9303160, doi:10.1016/0550-3213(93)90528-W
Matthias R. Gaberdiel, Horst G. Kausch, A Rational Logarithmic Conformal Field Theory, Phys.Lett. B 386 (1996) 131-137 arXiv:hep-th/9606050, doi:10.1016/0370-2693(96)00949-5
Review in:
Relation to the WZW-model:
On WZW models at fractional level:
Sunil Mukhi, Sudhakar Panda, Fractional-level current algebras and the classification of characters, Nuclear Physics B 338 1 (1990) 263-282 doi:10.1016/0550-3213(90)90632-N
Gregory Moore, Nicholas Read, p. 389 of: Nonabelions in the fractional quantum hall effect, Nuclear Physics B 360 2–3 (1991) 362-396 doi:10.1016/0550-3213(91)90407-O, pdf
(suggesting the fractional level as related to Laughlin wavefunctions of anyons)
Hidetoshi Awata, Yasuhiko Yamada, Fusion rules for the fractional level algebra, Mod. Phys. Lett. A 7 (1992) 1185-1196 spire:332974, doi:10.1142/S0217732392003645
P. Furlan, A. Ch. Ganchev, R. Paunov, Valentina B. Petkova, Solutions of the Knizhnik-Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models, Nucl. Phys. B394 (1993) 665-706 (arXiv:hep-th/9201080, doi:10.1016/0550-3213(93)90227-G)
J. L. Petersen, J. Rasmussen, M. Yu, Fusion, Crossing and Monodromy in Conformal Field Theory Based on Current Algebra with Fractional Level, Nucl. Phys. B481 (1996) 577-624 (arXiv:hep-th/9607129, doi:10.1016/S0550-3213(96)00506-8)
Boris Feigin, Feodor Malikov, Modular functor and representation theory of at a rational level, p. 357-405 in: Loday, Stasheff, Voronov (eds.) Operads: Proceedings of Renaissance Conferences, Contemporary Mathematics 202, AMS (1997) arXiv:q-alg/9511011, ams:conm-202
with a good review in:
On braided fusion categories formed by affine Lie algebra-representations at admissible fractional level:
On interpreting fractional level WZW models as logarithmic CFTs:
Matthias R. Gaberdiel, Fusion rules and logarithmic representations of a WZW model at fractional level, Nucl. Phys. B 618 (2001) 407-436 arXiv:hep-th/0105046, doi:10.1016/S0550-3213(01)00490-4)
Matthias R. Gaberdiel, Section 5 of: An algebraic approach to logarithmic conformal field theory, Int. J. Mod. Phys. A 18 (2003) 4593-4638 arXiv:hep-th/0111260, doi:10.1142/S0217751X03016860
David Ridout, : A Case Study, Nucl. Phys. B 814 (2009) 485-521 arXiv:0810.3532, doi:10.1016/j.nuclphysb.2009.01.008
Thomas Creutzig, David Ridout, Modular Data and Verlinde Formulae for Fractional Level WZW Models I, Nuclear Physics B 865 1 (2012) 83-114 arXiv:1205.6513, doi:10.1016/j.nuclphysb.2012.07.018
Thomas Creutzig, David Ridout, Modular Data and Verlinde Formulae for Fractional Level WZW Models II, Nuclear Physics B 875 2 (2013) 423-458 arXiv:1306.4388, doi:10.1016/j.nuclphysb.2013.07.008
Thomas Creutzig, David Ridout, Section 4 of: Logarithmic conformal field theory: beyond an introduction, J. Phys. A: Math. Theor. 46 (2013) 494006 (doi:10.1088/1751-8113/46/49/494006, arXiv:1303.0847)
Kazuya Kawasetsu, David Ridout, Relaxed highest-weight modules I: rank 1 cases, Commun. Math. Phys. 368 (2019) 627–663 arXiv:1803.01989, doi:10.1007/s00220-019-03305-x
Kazuya Kawasetsu, David Ridout, Relaxed highest-weight modules II: classifications for affine vertex algebras, Communications in Contemporary Mathematics, 24 05 (2022) 2150037 arXiv:1906.02935, doi:10.1142/S0219199721500371
Reviewed in:
David Ridout, Fractional Level WZW Models as Logarithmic CFTs (2010) pdf, pdf
David Ridout, Fractional-level WZW models (2020) pdf, pdf
In particular, the logarithmic model is essentially an admissible-level WZW model (namely at level ):
with a comprehensive account in:
On the model as the WZW model at fractional level and relation to the beta-gamma system:
and its lift to a logarithmic CFT:
On quasi-characters at fractional level:
Identification of would-be fractional level conformal blocks in twisted equivariant K-theory of configuration spaces of points:
Last revised on June 30, 2023 at 17:53:17. See the history of this page for a list of all contributions to it.