Characters and modular properties of permutation orbifolds

Abstract

Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is investigated.

A new rational conformal field theory extension of the fully degenerate W1+∞(m)

“…Λ of su(m) is defined in the following way: 4) where Λ i are the fundamental weights of su(m) and λ i are the Dynkin labels.…”

“…It was first introduced in [35,24] on RCFTs characterized as the tensor product of m copies of a given RCFT. The subject was further developed in [26,25,17,7,4,21,5], and it was also studied by using the approach of the m-reduction technique in [37,13,14]. A more complete classification has been recently presented in [2], where the orbifold construction is applied in the more general framework of the lattice vertex algebras (which are not simply tensor products of RCFTs).…”

“…In this paper, we show that our theory TM [14], characterized as the cyclic permutation 3 Where Z m is the rank m orthonormal lattice. 4 See Theorem 5.2 of [34]. 5 In particular, G is a finite subgroup of U (m).…”

Conformal Orbifold Theories and Braided Crossed G-Categories

“…4.3 are in contradiction to what can be derived from certain statements in [2], which in turn follow from [1]. This claim was wrong, being based on an erroneous deduction from the statements in [1,2]. I regret this mistake.…”

“…I regret this mistake. In fact, Bantay has provided me with a convincing argument to the effect that my Corollary 4.15 can also be deduced from the results of his earlier article [1]. His argument relies on the formula [1, Eq.…”