Logarithmic extensions of minimal models: characters and modular transformations

Abstract

We study logarithmic conformal field models that extend the (p,q) Virasoro minimal models. For coprime positive integers $p$ and $q$, the model is defined as the kernel of the two minimal-model screening operators. We identify the field content, construct the W-algebra W(p,q) that is the model symmetry (the maximal local algebra in the kernel), describe its irreducible modules, and find their characters. We then derive the SL(2,Z) representation on the space of torus amplitudes and study its properties. From the action of the screenings, we also identify the quantum group that is Kazhdan--Lusztig-dual to the logarithmic model.

43pp., AMSLaTeX++. V3: Some explanatory comments added, notational inaccuracies corrected, references added

References in corpus (6)

• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
• Virasoro representations and fusion for general augmented minimal models
• Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
• Logarithmic torus amplitudes
• A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness
• Modular invariance of vertex operator algebras satisfying C_2-cofiniteness

Cited by in corpus (22)

• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
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• Radford, Drinfeld, and Cardy boundary states in (1,p) logarithmic conformal field models
• Free fermion resolution of supergroup WZNW models
• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• W-Extended Logarithmic Minimal Models
• On the Percolation BCFT and the Crossing Probability of Watts
• On the triplet vertex algebra W(p)
• W-Extended Fusion Algebra of Critical Percolation
• Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model
• SLE local martingales in logarithmic representations
• Factorizable ribbon quantum groups in logarithmic conformal field theories
• On W-algebras associated to (2,p) minimal models and their representations
• Toward logarithmic extensions of ^sl(2)_k conformal field models
• A note on the logarithmic (p,p') fusion
• Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
• A differential U-module algebra for U=U_q sl(2) at an even root of unity
• Characters of coinvariants in (1,p) logarithmic models
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• Some Aspects of c=-2 Theory