The W_N minimal model classification

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W_3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W_3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of W_N(p,q) modular invariants. The W_3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.Comment: 25 page

On Fusion Algebras and Modular Matrices

We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix $S$, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the $A_r$ fusion algebra at level $k$. We prove that for many choices of rank $r$ and level $k$, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most $r$ and $k$. We also find new, systematic sources of zeros in the modular matrix $S$. In addition, we obtain a formula relating the entries of $S$ at fixed points, to entries of $S$ at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of $S$, and by the fusion (Verlinde) eigenvalues.Comment: 28 pages, plain Te

On the Classification of Diagonal Coset Modular Invariants

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.Comment: 24 pp (plain tex

Charges of Exceptionally Twisted Branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.Comment: 19 pages, 2 figures, LaTex2e, complete proofs of all statements, updated bibliograph

Measuring the cognition of firesetting individuals using explicit and implicit measures

This study examined un-apprehended deliberate firesetters’ cognition. Relative to non-firesetters, un-apprehended firesetters reported higher explicitly measured fire interest. However, their reaction times (RTs) on a fire interest implicit LDT were inconsistent with these findings. They did, however, display a pattern of LDT RTs consistent with Dangerous World and Fire is Powerful beliefs

Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.Comment: 16 pp, plain te

On parity functions in conformal field theories

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie algebras, for which we give two efficient formulas. We investigate the consequences of these for the modular invariance problem.Comment: 18 pages, no figure, LaTeX2