Logarithmic extensions of minimal models: characters and modular transformations

Details Logarithmic extensions of minimal models: characters and modular transformations Logarithmic extensions of minimal models: characters and modular transformations

2006-06-20

arxiv.org/abs/hep-th/0606196v3

Nucl.Phys.B757:303-343,2006

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.nuclphysb.2006.09.019

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.

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