Search

Let V be a simple vertex algebra of countable dimension, G be a finite automorphism group of V and σ be a central element of G. Assume that S is a finite set of inequivalent irreducible σ -twisted V -modules such that S is invariant under the action of G. Then there is a finite dimensional semisimple associative algebra A α (G , S) for a suitable 2-cocycle α naturally determined by the G -action on S such that (A α (G , S) , V G) form a dual pair on the sum M of σ -twisted V -modules in S in the sense that (1) the actions of A α (G , S) and V G on M commute, (2) each irreducible A α (G , S) -module appears in M , (3) the multiplicity space of each irreducible A α (G , S) -module is an irreducible V G -module, (4) the multiplicity spaces of different irreducible A α (G , S) -modules are inequivalent V G -modules. As applications, every irreducible V -module is a direct sum of finitely many irreducible V G -modules and irreducible V G -modules appearing in different G -orbits are inequivalent. This result generalizes many previous results. We also establish a bijection between subgroups of G and subalgebras of V containing V G. [ABSTRACT FROM AUTHOR]

We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA V G , and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to V G. Applying these methods to extremal lattices in d = 48 and d = 72 , we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states. [ABSTRACT FROM AUTHOR]

The restricted S -matrix of V G is determined for any regular vertex operator algebra V and finite automorphism group G of V. As an application, the S -matrices for cyclic permutation orbifolds of prime orders are computed. [ABSTRACT FROM AUTHOR]

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V G is regular. It is proved that every irreducible V G -module occurs in an irreducible g -twisted V -module for some g ∈ G . Moreover, the quantum dimensions of irreducible V G -modules are determined and a global dimension formula for V in terms of twisted modules is obtained. In particular, the orbifold theory conjecture is completely solved if G is solvable. [ABSTRACT FROM AUTHOR]

In this article, we first compute the quantum dimensions of irreducible ...-modules. These quantum dimensions give upper bounds on fusion rules among irreducible ...-modules. Together with the lower bounds obtained by Lam and the author, we determine explicitly fusion rules among all irreducible ...-modules of twisted type. This work completes the program for determining the fusion rules among irreducible ...-modules. [ABSTRACT FROM AUTHOR]

Let V be a simple vertex operator superalgebra and G a finite automorphism group of V containing the canonical automorphism σ such that V G is regular. It is proved that every irreducible V G -module occurs in an irreducible g -twisted V -module for some g ∈ G. Moreover, the quantum dimensions of irreducible V G -modules are determined, a global dimension formula for V in terms of twisted modules is obtained and a super quantum Galois theory is established. In addition the S -matrix of V G is computed. [ABSTRACT FROM AUTHOR]

To illustrate the general results of the previous paper, we discuss here a large concrete example of the orbifold-string theories of permutation-type. For each of the many subexamples, we focus on evaluation of the target space-time dimension$\hat{D}_j(\sigma)$, the target space-time signature and the target space-time symmetry of each cycle j in each twisted sector σ. We find in particular a gratifying space-time symmetry enhancement which naturally matches the space-time symmetry of each cycle to its space-time dimension. Although the orbifolds of ℤ2-permutation-type are naturally Lorentzian, we find that the target space-times associated with larger permutation groups can be Lorentzian, Euclidean and even null $(\hat{D}_j(\sigma) = 0)$, with varying space-time dimensions, signature and symmetry in a single orbifold. [ABSTRACT FROM AUTHOR]

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge $\hat{c}_j(\sigma) = 26f_j(\sigma)$, where fj(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge cj(σ) = 26. These tools are used to begin the study of the target space-time dimension $\hat{D}_j(\sigma)$ of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds. [ABSTRACT FROM AUTHOR]

This is the second in a series of papers which consider the orbifolds of permutation-type as candidates for new physical string systems at higher central charge. In the first paper, I worked out the extended actions of the twisted sectors of those orbifolds — which exhibit new permutation-twisted worldsheet gravities and correspondingly extended diffeomorphism groups. In this paper I begin the study of these systems as operator string theories, limiting the discussion for simplicity to the strings with ${\hat c} = 52$ matter (which are those governed by ℤ2-twisted permutation gravity). In particular, I present here a construction of the twisted reparametrization ghosts and new twisted BRST systems of all ${\hat c} = 52$ strings. The twisted BRST systems also imply new extended physical state conditions, whose analysis for individual ${\hat c} = 52$ strings is deferred to the next paper of the series. [ABSTRACT FROM AUTHOR]