Bits and Pieces in Logarithmic Conformal Field Theory

By M. Flohr. 2001

247 citations recorded by the source corpus.

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. These two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6f31df7ce6e8283ca1fadf585660a22e4d8c31b6

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Citations in the corpus

Logarithmic conformal field theory: a lattice approach (2013, background): “Combining this feature with criticality in 1 + 1 dimensions leads to the possibility of Jordan cells for the dilatation operator L0, and therefore, to profound physical and mathematical modifications of conformal invariance, giving rise to what is called Logarithmic Conformal Field Theory (LCFT) [20”
Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center (2005, background): “…p)-CONFORMAL FIELD THEORY, ITS CHARACTERS, AND SL(2, Z)-REPRESENTATIONS Logarithmic models of conformal field theory, of which the (1, p)-models are an example , were introduced in [24] and were considered, in particular, in [13] [8] [25] [9] [22] [23] [26] [15] (also see the references therein).”
Closed strings from decaying D-branes (2003, background): “Note that VB and V1 form a “logarithmic” pair [39,40,41].”
The GL(1|1) WZW-model: From supergeometry to logarithmic CFT (2005, background): “Many more details and references may be found in recent review articles [30, 31].”
Instability in cosmological topologically massive gravity at the chiral point (2008, background): “(For reviews see [14, 15]; for some applications to AdS/LCFT see [16–20].”
Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and their Generalized Modules (2010, methodology): “We refer the interested reader to the review articles [31, 42, 118] and [39], and references therein.”
Logarithmic extensions of minimal models: characters and modular transformations. (2006, unknown): “The OPE of W+(z) andW−(z) is (4.2) W+(z)W−(w) = Sp+,p−(T ) (z − w)7p+p−−3p+−3p−+1 + less singular terms, whereSp+,p−(T ) is the vacuum singular vector — the polynomial of degree 1 2 (p+− 1)· (p− − 1) in T and∂nT , n> 1, such thatSp+,p−(T ) = 0 is the polynomial relation for the energy–momentum tenso”
Logarithmic conformal field theory: beyond an introduction (2013, background): “have progressed rather rapidly with many of the standard features of rational conformal ﬁeld the ory now understood in the logarithmic setting. In particular, there are two ﬁne reviews of the subject [7,8] which focus on, among other things, modular transformations and module structure, mostly for a”