Logarithmic Conformal Field Theory With Boundary

Kawai, Shinsuke

doi:10.1142/s0217751x03016884

Cited by 26 publications

(34 citation statements)

References 67 publications

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“…Under the assumption that the modular differential equation is in fact of order 3p − 1 = 8, we can determine it uniquely by requiring it to be solved by this vacuum character. Explicitly we find − 5897 124416 E 4 (q)E 6 (q)cod (6) cod (4) cod (2) + 10889 55296 (E 4 (q)) 2 cod (8) cod (6) cod (4) cod (2) + 157 432 E 6 (q)cod (10) cod (8) cod (6) cod (4) cod (2) − 21 16 E 4 (q)cod (12) cod (10) cod (8) cod (6) cod (4) cod (2) + cod (16) cod (14) cod (12) cod (10) cod (8) cod (6) cod (4) cod (2) T (q) .…”

Section: Solving the Modular Differential Equationmentioning

confidence: 88%

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Logarithmic torus amplitudes

Flohr¹,

Gaberdiel²

2006

J. Phys. A: Math. Gen.

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For the example of the logarithmic triplet theory at c = −2 the chiral vacuum torus amplitudes are analysed. It is found that the space of these torus amplitudes is spanned by the characters of the irreducible representations, as well as a function that can be associated to the logarithmic extension of the vacuum representation. A few implications and generalisations of this result are discussed.1. Introduction. During the last twenty years much has been understood about the structure of rational conformal field theories. Rational conformal field theories are characterised by the property that they have only finitely many irreducible highest weight representations of the chiral algebra (or vertex operator algebra), and that every highest weight representation is completely decomposable into irreducible representations. The structure of these theories is well understood: in particular, the characters of the irreducible representations transform into one another under modular transformations [1] (see also [2]), and the modular S-matrix determines the fusion rules via the Verlinde formula [3]. (A general proof for this has only recently been given in [4].) On the other hand, it is clear that rational conformal field theories are rather special, and it is therefore important to understand the structure of more general classes of conformal field theories. One such class are the (rational) logarithmic theories that possess only finitely many indecomposable representations, but for which not all highest weight representations are completely decomposable. The name 'logarithmic' comes from the fact that their chiral correlation functions typically have logarithmic branch cuts. The first example of a (nonrational) logarithmic conformal field theory was found in [5] (see also [6]), and the first rational example (that shall also concern us in this paper) was constructed in [7]; for some recent reviews see [8,9,10]. From a physics point of view, logarithmic conformal field theories appear naturally in various models of statistical physics, for example in the theory

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Section: Solving the Modular Differential Equationmentioning

confidence: 88%

“…The modular differential equation. The above calculation leading to (10) implies that in Zhu's algebra we have the relation…”

mentioning

confidence: 94%

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Logarithmic torus amplitudes

Flohr¹,

Gaberdiel²

2006

J. Phys. A: Math. Gen.

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“…The references given above can serve as a starting point for the reader. More comprehensive discussions can be found in the review articles [37][38][39][40][41]. A special class of 2d logCFTs, in the form of WZW and sigma models on superspaces, is reviewed in [42].…”

Section: Jhep10(2017)201mentioning

confidence: 99%

“…After defining the functions 39) it is possible to write the functions K abc in the following compact form:…”

Section: Jhep10(2017)201mentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is modelindependent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

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Notes on generalised nullvectors in logarithmic CFT

Eberle

Flohr

2006

Nuclear Physics B

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In these notes we discuss the procedure how to calculate nullvectors in general indecomposable representations which are encountered in logarithmic conformal field theories. In particular, we do not make use of any of the restrictions which have been imposed in logarithmic nullvector calculations up to now, especially the quasi-primarity of all Jordan cell fields.For the quite well-studied c p,1 models we calculate examples of logarithmic nullvectors which have not been accessible to the older methods and recover the known representation structure. Furthermore, we calculate logarithmic nullvectors in the up to now almost unexplored general augmented c p,q models and use these to find bounds on their possible representation structures. *

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Logarithmic Conformal Field Theory With Boundary

Cited by 26 publications

References 67 publications

Logarithmic torus amplitudes

Logarithmic torus amplitudes

The ABC (in any D) of logarithmic CFT

Notes on generalised nullvectors in logarithmic CFT

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