Systematic Approach to Cyclic Orbifolds

Borisov, Lev A.; Halpern, M.B.; Schweigert, Christoph

doi:10.1142/s0217751x98000044

Cited by 136 publications

(389 citation statements)

References 59 publications

(110 reference statements)

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“…We will confirm the results in §4.6 of [5]. Let us first simply our notations by introducing similar notations in [5]. Let (λ0) := (λ, −1, 0), (λ1) := (λ, −1, 1).…”

Section: N=2 Casesupporting

confidence: 75%

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Solitons in Affine and Permutation Orbifolds

Kač

Longo

2004

Commun. Math. Phys.

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We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to prove a number of conjectures: in the affine orbifold case we clarify the issue of "fixed point resolutions"; in the permutation orbifold case we determine all irreducible representations of the orbifold, and we also determine the fusion rules in a nontrivial case, which imply an integral property of chiral data for any completely rational conformal net.

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“…We will confirm the results in §4.6 of [5]. Let us first simply our notations by introducing similar notations in [5]. Let (λ0) := (λ, −1, 0), (λ1) := (λ, −1, 1).…”

Section: N=2 Casesupporting

confidence: 75%

“…Cor. 9.9), proving a conjecture in the paper [5], that contained the first computations leading to correct fusion rules.…”

Section: Introductionmentioning

confidence: 59%

Solitons in Affine and Permutation Orbifolds

Kač

Longo

2004

Commun. Math. Phys.

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“…for superstring orbifolds of permutation-type. There is a surprisingly large variety of orbifolds of permutation-type, including the permutation orbifolds themselves [1][2][3][4][5][6]11,16], the orientation orbifolds [12,13,15,16], the open-string permutation orbifolds [14] and their T -duals [15,16], the generalized permutation orbifolds [15,16] and others. A short review of these varieties is included in Ref.…”

Section: Introductionmentioning

confidence: 99%

THE ORBIFOLDS OF PERMUTATION-TYPE AS PHYSICAL STRING SYSTEMS AT MULTIPLES OF c = 26 II: THE TWISTED BRST SYSTEMS OF ${\hat c} = 52$ MATTER

Halpern

2007

Int. J. Mod. Phys. A

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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 world-sheet 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 withĉ = 52 matter (which are those governed by Z 2 -twisted permutation gravity). In particular, I present here a construction of the twisted reparametrization ghosts and new twisted BRST systems of allĉ = 52 strings. The twisted BRST systems also imply new extended physical state conditions, whose analysis for individualĉ = 52 strings is deferred to the next paper of the series.

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“…Formulae for the dimensions of spaces of conformal blocks in permutation orbifolds have been given in [BHS98,Ban98]. It is easy to see that these formulae imply that dimension of the spaces of conformal three-point blocks of the equivariant theory on the sphere involving two objects in the twisted sector are given by the dimension of the spaces of four-point blocks on the sphere for C. This nicely follows from the geometry of the cover functor: the total space of the relevant cover is isomorphic to the four-punctured sphere.…”

Section: The Tensor Productmentioning

confidence: 99%

A geometric construction for permutation equivariant categories from modular functors

Barmeier

Schweigert

2011

Transformation Groups

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Let G be a finite group. Given a finite G-set X and a modular tensor category C, we construct a weak G-equivariant fusion category C X , called the permutation equivariant tensor category. The construction is geometric and uses the formalism of modular functors. As an application, we concretely work out a complete set of structure morphisms for Z/2-permutation equivariant categories, finishing thereby a program we initiated in [BFRS10].

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Systematic Approach to Cyclic Orbifolds

Cited by 136 publications

References 59 publications

Solitons in Affine and Permutation Orbifolds

Solitons in Affine and Permutation Orbifolds

THE ORBIFOLDS OF PERMUTATION-TYPE AS PHYSICAL STRING SYSTEMS AT MULTIPLES OF c = 26 II: THE TWISTED BRST SYSTEMS OF ${\hat c} = 52$ MATTER

A geometric construction for permutation equivariant categories from modular functors

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