Ho-Kim, Q. (Quang), 1938-Elementary particles and their interactions: concepts and phenomena / Quang Ho-Kim, Xuan-Yem Pham. p. cm. Includes bibliographical references and index. ISBN 3-540-63667-6 (alk. paper) 1. Particles (Nuclear physics) 2.. Nuclear reactions. I.

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Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras g (1) of g = A 2 , A 1 + A 1 , G 2 , and C 2 . Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for A 2 at levels ≤ 32, for G 2 at levels ≤ 31, for C 2 at levels ≤ 26, and for A 1 + A 1 at levels k 1 = k 2 ≤ 21. This work thus completes a recent A 2 classification proof, where the levels k = 3, 5, 6, 9, 12, 15, 21 had been left out. We also compute the dimension of the (Weyl-folded) commutant for these algebras and levels.

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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 been completely classified. We also find all physical modular invariants for su(2) k 1 × su(2) k 2 , for 22 > k 1 > k 2 , and k 1 = 28, k 2 < 22, completing the classification of ref. [9].