The Low Level Modular Invariant Partition Functions of Rank-Two Algebras
نویسنده
چکیده
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 work thus completes a recent A2 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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