Exclusion statistics for non-abelian quantum Hall states

We determine the exclusion statistics properties of the fundamental edge quasi-particles over a specific \nu=\half non-abelian quantum Hall state known as the pfaffian. The fundamental excitations are the edge electrons of charge $-e$ and the edge quasi-holes of charge $+{e \over 4}$. We explicitly determine thermodynamic distribution functions and establish a duality which generalizes the duality for fractional exclusion statistics in the sense of Haldane.Comment: LaTeX, 4 pages, no figures; results for 1/q pfaffian adde

Induced (N,0) supergravity as a constrained Osp(N,2) WZWN model and its effective action

A chiral $(N,0)$ supergravity theory in d=2 dimensions for any $N$ and its induced action can be obtained by constraining the currents of an Osp(N$|$2) WZWN model. The underlying symmetry algebras are the nonlinear SO(N) superconformal algebras of Knizhnik and Bershadsky. The case $N=3$ is worked out in detail. We show that by adding quantum corrections to the classical transformation rules, the gauge algebra on gauge fields and currents closes. Integrability conditions on Ward identities are derived. The effective action is computed at one loop. It is finite, and can be obtained from the induced action by rescaling the central charge and fields by finite Z factors.Comment: 23

On the vanishing of Tor of the absolute integral closure

Let $R$ be an excellent local domain of positive characteristic with residue field $k$ and let $R^+$ be its absolute integral closure. If $\text{Tor}^R_1(R^+,k)$ vanishes, then $R$ is Cohen-Macaulay, normal, F-rational and F-pure. If $R$ has at most an isolated singularity or has dimension at most two, then $R$ is regular

Comment on the paper ``The universal chiral partition function for exclusion statistics''

I comment on the paper hep-th/9808013 by A. Berkovich and B.M. McCoy.Comment: 1 page, revtex, original comment replaced by brief statemen