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Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists
This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through
TFT construction of RCFT correlators I: Partition functions
We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore-Seiberg data of the
From Dynkin diagram symmetries to fixed point structures
Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra g induces an automorphism of g and a mappingτω between highest weight modules of g. For a large class of such Dynkin
Kramers-wannier duality from conformal defects.
We demonstrate that the fusion algebra of conformal defects of a two-dimensional conformal field theory contains information about the internal symmetries of the theory and allows one to read off
DUALITY AND DEFECTS IN RATIONAL CONFORMAL FIELD THEORY
We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects
BOUNDARIES, CROSSCAPS AND SIMPLE CURRENTS
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
Correspondences of ribbon categories
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories.
TFT construction of RCFT correlators V: Proof of modular invariance and factorisation
The correlators of two-dimensional rational conformal field theories that are obtained in the TFT construction of [FRSI,FRSII,FRSIV] are shown to be invariant under the action of the relative modul
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