On the Classification of Diagonal Coset Modular Invariants

Abstract

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3{)}_k\oplus su(3{)}_1/su(3{)}_{k+1}$ for all positive integer level $k$, and $su(2{)}_k\oplus su(2{)}_{\ell }/su(2{)}_{k+\ell }$ for all $k$ and infinitely many $\ell$ (in fact, for each $k$ a positive density of $\ell$). Of all these classifications, only that for $su(2{)}_k\oplus su(2{)}_1/su(2{)}_{k+1}$ had been known. Our lists include many new invariants.

24 pp (plain tex)

References in corpus (8)

• The Classification of Affine SU(3) Modular Invariant Partition Functions
• su(3)k fusion coefficients
• WZW Commutants, Lattices, and Level 1 Partition Functions
• The Classification of SU(3) Modular Invariants Revisited
• Implications of an arithmetical symmetry of the commutant for modular invariants
• Towards a Classification of su(2)$⨁\cdots ⨁$su(2) Modular Invariant Partition Functions
• Field Identification in Non-Unitary Diagonal Cosets
• The Low Level Modular Invariant Partition Functions of Rank-Two Algebras

Cited by in corpus (13)

• The Gravity Dual of the Ising Model
• The resolution of field identification fixed points in diagonal coset theories
• From CFT's to Graphs
• Organizing boundary RG flows
• The Classification of SU(3) Modular Invariants Revisited
• $U(1{)}^m$ modular invariants, N=2 minimal models, and the quantum Hall effect
• On the complete classification of the unitary N=2 minimal superconformal field theories
• Towards a Classification of su(2)$⨁\cdots ⨁$su(2) Modular Invariant Partition Functions
• Novel construction of boundary states in coset conformal field theories
• The W_N minimal model classification
• Coset construction of logarithmic minimal models: branching rules and branching functions
• Conformal embeddings and higher-spin bulk duals
• Heterotic Modular Invariants and Level--Rank Duality