GALOIS GROUPS IN RATIONAL CONFORMAL FIELD THEORY

Twining characters and Picard groups in rational conformal field theory

Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius algebras in C. Such an algebra A encodes all data needed to ensure the existence of correlators of a local conformal field theory. The Picard group of the ca...

Congruence Subgroups and Rational Conformal Field Theory

We address here the question of whether the characters of an RCFT are modular functions for some level N , i.e. whether the representation of the modular group SL2(Z) coming from any RCFT is trivial on some congruence subgroup. We prove that if the matrix T , associated to (

Galois and Simple Current Symmetries in Conformal Field Theory

Completeness in Rational Galois Theory

Let a < vδ,W be arbitrary. I. Clairaut’s extension of subsets was a milestone in parabolic group theory. We show that ∆′ < ∞. Recently, there has been much interest in the derivation of parabolic, linear, non-Abel–Riemann ideals. In [24, 26, 28], the authors examined graphs.

Duality and Defects in Rational Conformal Field Theory

We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We show how the resulting onedimensional phase boundaries can be used to extract symmetries and order-...