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.

7 pages, LaTeX

References in corpus (2)

• Elliptic Genera of Symmetric Products and Second Quantized Strings
• The Frobenius-Schur indicator in Conformal Field Theory

Cited by in corpus (68)

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• Twisted sectors for tensor product vertex operator algebras associated to permutation groups
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• String Universality for Permutation Orbifolds
• Permutation orbifolds
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Permutation orbifolds and holography
• Universality of Sparse $d>2$ Conformal Field Theory at Large $N$
• Generalized twisted modules associated to general automorphisms of a vertex operator algebra
• Conformal Orbifold Theories and Braided Crossed G-Categories
• Boundary States of c=1 and 3/2 Rational Conformal Field Theories
• The Spectrum of Boundary States in Symmetric Orbifolds
• Orbifold analysis of broken bulk symmetries
• General Virasoro Construction on Orbifold Affine Algebra
• D-branes in an asymmetric orbifold
• Boundaries, defects and Frobenius algebras
• The General Twisted Open WZW String
• Evolution of Entanglement Entropy in Orbifold CFTs
• Out-of-Time-Ordered Correlators in $(T^2{)}^n/{\mathbb{Z}}_n$
• The Outer-Automorphic WZW Orbifolds on so(2n), including Five Triality Orbifolds on so(8)
• More About All Current-Algebraic Orbifolds
• Bound States of Little Strings and Symmetric Orbifold CFTs
• Cyclic Coset Orbifolds
• Integers in the open string
• Extended Operator Algebra and Reducibility in the WZW Permutation Orbifolds
• Permutation Orbifolds in the large N Limit
• Frobenius-Schur Indicators, the Klein-bottle Amplitude, and the Principle of Orbifold Covariance
• $C_2$-cofiniteness of 2-cyclic permutation orbifold models
• On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors
• Twisted Einstein Tensors and Orbifold Geometry
• C_2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds
• Vanishing of categorical obstructions for permutation orbifolds
• A note on permutation twist defects in topological bilayer phases
• A Basic Class of Twisted Open WZW Strings
• Permutation Orbifolds of the Heisenberg Vertex Algebra $\mathcal{H}(3)$
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Fixed Point Resolution in Extensions of Permutation Orbifolds
• Open String on Symmetric Product
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26. I.Extended Actions and New Twisted World-Sheet Gravities
• A Short Guide to Orbifold Deconstruction
• Fusion Rules for $\mathbb{Z}/2\mathbb{Z}$ Permutation Gauging
• Dimensional Reduction, Extended Topological Field Theories and Orbifoldization
• Limits of Vertex Algebras and Large N Factorization
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• Complete Analysis of Extensions of $D(n{)}_1$ Permutation Orbifolds
• Formula for Fixed Point Resolution Matrix of Permutation Orbifolds
• DLCQ Strings, Twist Fields and One-Loop Correlators on a Permutation Orbifold
• The operator algebra of cyclic orbifolds
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $\mathbf{c}=26$ V. Cyclic Permutation Orbifolds
• On permutation-twisted free fermions and two conjectures
• The torus and the Klein Bottle amplitude of permutation orbifolds
• 2-permutations of lattice vertex operator algebras: Higher rank
• The 3-permutation orbifold of a lattice vertex operator algebra
• The orbifold transform and its applications
• Cyclic permutations of lattice vertex operator algebras
• D-branes in ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathbb{T}}^4$ at $k=1$ and their holographic duals
• Character relations and replication identities in 2d Conformal Field Theory
• Permutation Orbifolds in Conformal Field Theories and String Theory
• Open Superstring on Symmetric Product
• A new Rational Conformal Field Theory extension of the fully degenerate W_{1+\infty}^{(m)}
• Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case
• S-matrix in orbifold theory
• Orbifold deconstruction: a computational approach
• An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras