logarithmic CFT




A class of 2d conformal field theories which are not rational conformal field theories but are the closest to them in the class of irrational. The appearance of the logarithmic term corresponds to the nontrivial 2×22\times 2 Jordan blocks for the L 0L_0 operator. Many models of LCFT seem to be related to the quantum groups at even root of unity.


  • John Cardy, Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications, arXiv:1302.4279
  • 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 W p,pW_{p,p'}, arxiv/1202.6667; C 2C_2-cofinite W-algebras and their logarithmic representations_, arxiv/1212.6771; Logarithmic intertwining operators and W(2,2p1)W(2,2p-1)-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 sl^(2)\widehat{sl}(2) 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
  • B L 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; Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center, Commun. Math. Phys. 265 (2006) 47–93; Kazhdan–Lusztig correspondence for the representation category of the triplet WW-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
  • David Ridout, Simon Wood, Bosonic ghosts at c=2c=2 as a logarithmic CFT, arxiv/1408.4185

On the Verlinde formula for logarithmic CFTs:

On the braided tensor categories corresponding to logarithmic CFTs:

  • Thomas Creutzig, Simon Lentner, Matthew Rupert, Characterizing braided tensor categories associated to logarithmic vertex operator algebras (arXiv:2104.13262)
category: physics

Last revised on April 28, 2021 at 03:56:43. See the history of this page for a list of all contributions to it.