The Classification of Affine SU ( 3 ) Modular Invariant Partition Functions
نویسنده
چکیده
A complete classification of the WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of SU(2), and level 1 of all simple algebras. In this paper we solve the classification problem for SU(3) modular invariant partition functions. Our approach will also be applicable to other affine Lie algebras, and we include some preliminary work in that direction, including a sketch of a new proof for SU(2).
منابع مشابه
An Observation on Finite Groups and WZW Modular Invariants
In this short note, inspired by much recent activity centred around attempts to formulate various correspondences between the classification of affine SU(k) WZW modular-invariant partition functions and that of discrete finite subgroups of SU(k), we present a small and perhaps interesting observation in this light. In particular we show how the groups generated by the permutation of the terms i...
متن کاملSU (3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU (3) modular invariants
We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.
متن کاملModular Invariant Partition Functions in the Quantum Hall Effect
We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable...
متن کاملThe Rank Four Heterotic Modular Invariant Partition Functions
In this paper, we develop several general techniques to investigate modular invariants of conformal field theories whose algebras of the holomorphic and anti-holomorphic sectors are different. As an application, we find all such “heterotic” WZNW physical invariants of (horizontal) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank ≤ 3 have b...
متن کاملThe Low Level Modular Invariant Partition Functions of Rank-Two Algebras
Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras g of g = A2, A1 + A1, G2, and C2. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for A2 at levels ≤ 32, for G2 at levels ≤ 31, for C2 at levels ≤ 26, and for A1 + A1 at levels k1 = k2 ≤ 21. This wo...
متن کامل