Wzw Fusion Rings in the Limit of Infinite Level
نویسندگان
چکیده
We show that the WZW fusion rings at finite levels form a projective system with respect to the partial ordering provided by divisibility of the height, i.e. the level shifted by a constant. From this projective system we obtain WZW fusion rings in the limit of infinite level. This projective limit constitutes a mathematically welldefined prescription for the ‘classical limit’ of WZW theories which replaces the naive idea of ‘sending the level to infinity’. The projective limit can be endowed with a natural topology, which plays an important rôle for studying its structure. The representation theory of the limit can be worked out by considering the associated fusion algebra; this way we obtain in particular an analogue of the Verlinde formula. —————— $ Heisenberg fellow
منابع مشابه
Presentations of Wess-zumino-witten Fusion Rings
The fusion rings of Wess-Zumino-Witten models are re-examined. Attention is drawn to the difference between fusion rings over Z (which are often of greater importance in applications) and fusion algebras over C. Complete proofs are given characterising the fusion algebras (over C) of the SU (r + 1) and Sp (2r) models in terms of the fusion potentials, and it is shown that the analagous potentia...
متن کاملOn the tensionless limit of gauged WZW models
The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional bl...
متن کاملRings with a setwise polynomial-like condition
Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.
متن کاملThe Entanglement Entropy of Solvable Lattice Models
We consider the spin κ/2 analogue of the XXZ quantum spin chain. We compute the entanglement entropy S associated with splitting the infinite chain into two semi-infinite pieces. In the scaling limit, we find S ≃ cκ 6 ln(ξ) + g + · · · . Here ξ is the correlation length and cκ = 3κ κ+2 is the central charge associated with the ŝl2 WZW model at level κ. g is the boundary entropy of the WZW model...
متن کاملExact chiral ring of AdS3/CFT2
We carry out an exact worldsheet computation of tree level three-point correlators of chiral operators in type IIB string theory on AdS3×S×T 4 with NS-NS flux. We present a simple representation for the string chiral operators in the coordinate basis of the dual boundary CFT. Striking cancelations occur between the three-point functions of the H3 and the SU(2) WZW models which result in a simpl...
متن کامل