Related papers: Crystallising the Depth Rule for WZNW Fusion Coeff…
The depth rule is a level truncation of tensor product coefficients expected to be sufficient for the evaluation of fusion coefficients. We reformulate the depth rule in a precise way, and show how, in principle, it can be used to calculate…
Recently (hep-th/9307183) we showed that for the case of the WZW- and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral…
We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its…
The fusion products of admissible representations of the su(2) WZW model at the fractional level k=-4/3 are analysed. It is found that some fusion products define representations for which the spectrum of L_0 is not bounded from below.…
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…
Fusion rules for Wess-Zumino-Witten (WZW) models at fractional level can be defined in two ways, with distinct results. The Verlinde formula yields fusion coefficients that can be negative. These signs cancel in coset fusion rules, however.…
A closed formula for the structure constants in the SL(2,C)/SU(2) WZNW model is derived by a method previously used in Liouville theory. With the help of a reflection amplitude that follows from the structure constants one obtains a…
We investigate the depth of the tensor product of finitely generated modules over local rings. One of the main ingredients of our approach is a lifting construction introduced by Huneke, Jorgensen, and Wiegand. We recover a result of…
In this paper we determine the fusion rules of the logarithmic ${\calW}_{p,q}$ triplet theory and construct the Grothendieck group with subgroups for which consistent product structures can be defined. The fusion rules are then used to…
The fusion rule gives the dimensions of spaces of conformal blocks in the WZW theory. We prove a dimension formula similar to the fusion rulefor spaces of coinvariants of affine Lie algebras g^. An equivalence of filtered spaces is…
We show the $L^2$-Wasserstein contraction for the transition kernel of a discretised diffusion process, under a contractivity at infinity condition on the drift and a sufficiently high diffusivity requirement. This extends recent results…
We apply the recently developped analytical methods for computing the boundary entropy, or the g-function, in integrable theories with non-diagonal scattering. We consider the particular case of the current-perturbed $SU(2)_k$ WZNW model…
We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain…
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…
There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped with an integral gradation. It is explained how the different approaches to these dynamical systems are related by gauge transformations. Combining Gauss…
In this paper we introduce a new formulation of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of prefixes of infinite sequences from…
This is the first of two articles devoted to a comprehensive exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product…
Proving formula depth lower bounds is a fundamental challenge in complexity theory, with the strongest known bound of $(3 - o(1))\log n$ established by Hastad over 25 years ago. The Karchmer-Raz-Wigderson (KRW) conjecture offers a promising…
We investigate the low density limit of the Homogeneous Electron system, often called the {\it Strictly Correlated} regime. We begin with a systematic presentation of the expansion around infinite $r_S$, based on the first quantized…
A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is presented which, in the limit $k \rightarrow \infty$, turns into a simple and compact expression for the $su(3)$ tensor product coefficients. The derivation is based…