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Related papers: Fusion Rules for Extended Current Algebras

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We study the operator product expansion in the AdS$_3$ WZNW model. The OPE of primary fields and their spectral flow images is computed from the analytic continuation of the expressions in the H$_3^+$ WZNW model, adding spectral flow. We…

High Energy Physics - Theory · Physics 2009-04-22 Walter H. Baron , Carmen A. Núñez

The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a…

High Energy Physics - Theory · Physics 2011-07-19 Ioannis Smyrnakis

We introduce the notion of (nondegenerate) strongly-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group whose kernel contains a congruence…

High Energy Physics - Theory · Physics 2009-09-25 Wolfgang Eholzer

Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of…

High Energy Physics - Theory · Physics 2022-03-23 Anh-Khoi Trinh

The generalization to N=1 superconformal minimal models of the relation between the modular transformation matrix and the fusion rules in rational conformal field theories, the Verlinde theorem, is shown to provide complete information…

High Energy Physics - Theory · Physics 2009-03-27 Pablo Minces , Ali Namazie , Carmen Nunez

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…

High Energy Physics - Theory · Physics 2007-05-23 J. Fuchs , A. N. Schellekens , C. Schweigert

In this paper we study modular $G$-equivariant fusion categories and their extended Verlinde algebras. We dicuss settings in which fusion rules are diagonalizable. In particular, when $G = \mathbb{Z}_{2}$ we generalize the Verlinde formula.…

Quantum Algebra · Mathematics 2009-09-29 Vincent Graziano

One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings--the Penrose, octagonal, and pinwheel tilings are famous examples. We present a…

Mathematical Physics · Physics 2013-11-22 Natalie Priebe Frank

Through well-motivated models in particle physics, we demonstrate the power of a general class of selection rules arising from non-invertible fusion algebras that are only exact at low orders in perturbation theory. Surprisingly, these…

High Energy Physics - Phenomenology · Physics 2025-10-07 Motoo Suzuki , Ling-Xiao Xu

Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…

High Energy Physics - Theory · Physics 2025-01-20 Jaroslav Scheinpflug , Martin Schnabl

We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punctured trapezoidal rule, and then derive error expansions. We…

Numerical Analysis · Mathematics 2022-08-30 Federico Izzo , Olof Runborg , Richard Tsai

The algebraic or ring structure of anyons, called the fusion rule, is one of the most fundamental research interests in contemporary studies on topological orders (TOs) and the corresponding conformal field theories (CFTs). Recently, the…

High Energy Physics - Theory · Physics 2026-03-18 Yoshiki Fukusumi

We outline the structure of boundary conditions in conformal field theory. A boundary condition is specified by a consistent collection of reflection coefficients for bulk fields on the disk together with a choice of an automorphism \omega…

High Energy Physics - Theory · Physics 2007-05-23 J. Fuchs , C. Schweigert

We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably…

High Energy Physics - Theory · Physics 2011-06-27 Jorgen Rasmussen , Paul A. Pearce

The effective field theory (EFT) framework is a precise approximation procedure when the inherent assumptions of a large-scale separation between the Standard Model (SM) and new interactions alongside perturbativity are realised.…

High Energy Physics - Phenomenology · Physics 2024-03-22 Upalaparna Banerjee , Joydeep Chakrabortty , Christoph Englert , Wrishik Naskar , Shakeel Ur Rahaman , Michael Spannowsky

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary…

Quantum Algebra · Mathematics 2014-01-29 Drazen Adamovic , Ozren Perse

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the…

High Energy Physics - Theory · Physics 2009-10-28 Roger E. Behrend , Paul A. Pearce , David L. O'Brien

We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for…

Mathematical Physics · Physics 2015-08-13 Niklas Beisert , Marius de Leeuw , Panchali Nag

We propose using smeared boundary states $e^{-\tau H}|\cal B\rangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches…

High Energy Physics - Theory · Physics 2017-08-15 John Cardy

Universal formulas for the boundary and crosscap coefficients are presented, which are valid for all symmetric simple current modifications of the charge conjugation invariant of any rational conformal field theory.

High Energy Physics - Theory · Physics 2008-11-26 J. Fuchs , L. R. Huiszoon , A. N. Schellekens , C. Schweigert , J. Walcher