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

Electromagnetic wave scattering on imperfect cloaking devices

Cloaking devices based on the coordinate transform approach enable, in principle, a perfect concealment of a region in space provided that the material composing the cloaking shell meets certain criteria. To achieve ideal cloaking it is necessary that the shell material parameters have singular values on the surface bounding the cloaked region which is unphysical. In this paper we assume finite values of cloak parameters and apply the scattering theory formalism to give an estimate of the overall performance of an 'imperfect' cloak. We perform full-wave numerical calculations and use our theoretical results to discuss them