Galois currents and the projective kernel in Rational Conformal Field Theory
@article{Bantay2003GaloisCA, title={Galois currents and the projective kernel in Rational Conformal Field Theory}, author={Peter Bantay}, journal={arXiv: High Energy Physics - Theory}, year={2003} }
The notion of Galois currents in Rational Conformal Field Theory is introduced and illustrated on simple examples. This leads to a natural partition of all theories into two classes, depending on the existence of a non-trivial Galois current. As an application, the projective kernel of a RCFT, i.e. the set of all modular transformations represented by scalar multiples of the identity, is described in terms of a small set of easily computable invariants.
7 Citations
On non-semisimple fusion rules and tensor categories
- Mathematics
- 2006
Category theoretic aspects of non-rational conformal field theories are discussed. We consider the case that the category C of chiral sectors is a finite tensor category, i.e. a rigid monoidal…
Simple Current Actions of Cyclic Groups
- Mathematics
- 2005
Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility…
Hopf Algebras and Congruence Subgroups
- Mathematics
- 2007
We prove that the kernel of the natural action of the modular group on the center of the Drinfel'd double of a semisimple Hopf algebra is a congruence subgroup. To do this, we introduce a class of…
Simple current symmetries in RCFT
- Mathematics
- 2004
The question ``Which abelian permutation groups arise as group of simple currents in Rational Conformal Field Theory?'' is investigated using the formalism of weighted permutation actions. After a…
R A ] 3 O ct 2 00 7 Hopf Algebras and Congruence Subgroups
- Mathematics
- 2008
We prove that the kernel of the natural action of the modular group on the center of the Drinfel’d double of a semisimple Hopf algebra is a congruence subgroup. To do this, we introduce a class of…
References
SHOWING 1-10 OF 13 REFERENCES
The Kernel of the Modular Representation and the Galois Action in RCFT
- Mathematics
- 2003
Abstract: It is shown that for the modular representations associated to Rational Conformal Field Theories, the kernel is a congruence subgroup whose level equals the order of the Dehn-twist. An…
Markov traces and II1 factors in conformal field theory
- Mathematics
- 1991
Using the duality equations of Moore and Seiberg we define for every primary field in a Rational Conformal Field Theory a proper Markov trace and hence a knot invariant. Next we define two nested…
Modular invariance and uniqueness of conformal characters
- Mathematics
- 1995
We show that the conformal characters of various rational models ofW-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result…
Simple Currents, Modular Invariants and Fixed Points
- Mathematics
- 1990
We review the use of simple currents in constructing modular invariant partition functions and the problem of resolving their fixed points. We present some new results, in particular regarding fixed…
Classical and quantum conformal field theory
- Mathematics
- 1989
We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field…
On the classification of modular fusion algebras
- Mathematics
- 1995
AbstractWe introduce the notion of (nondegenerate) strongly-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the…