 School of Mathematics and Statistics  Research Publications
School of Mathematics and Statistics  Research Publications
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ItemExclusion statistics in conformal field theory and the UCPF for WZW modelsBouwknegt, P ; Chim, L ; Ridout, D (ELSEVIER, 20000424)

ItemConvergence properties of gradient descent noise reductionRidout, D ; Judd, K (ELSEVIER, 20020501)

ItemDbranes on group manifolds and fusion ringsBouwknegt, P ; Dawson, P ; Ridout, D (SPRINGER, 200212)

ItemA note on the equality of algebraic and geometric Dbrane charges in WZW modelsBouwknegt, P ; Ridout, D (SPRINGER, 200405)

ItemPresentations of WessZuminoWitten fusion ringsBouwknegt, P ; Ridout, D (WORLD SCIENTIFIC PUBL CO PTE LTD, 200603)The fusion rings of the Wess–Zumino–Witten models are reexamined. Attention is drawn to the difference between fusion rings over ℤ (which are often of greater importance in applications) and fusion algebras over ℂ. Complete proofs are given by characterizing the fusion algebras (over ℂ) of the SU (r+1) and Sp (2r) models in terms of the fusion potentials, and it is shown that the analagous potentials cannot describe the fusion algebras of the other models. This explains why no other representationtheoretic fusion potentials have been found. Instead, explicit generators are then constructed for general WZW fusion rings (over ℤ). The Jacobi–Trudy identity and its Sp (2r) analogue are used to derive the known fusion potentials. This formalism is then extended to the WZW models over the spin groups of odd rank, and explicit presentations of the corresponding fusion rings are given. The analogues of the Jacobi–Trudy identity for the spinor representations (for all ranks) are derived for this purpose, and may be of independent interest.

ItemThe extended algebra of the SU(2) WessZuminoWitten modelsMathieu, P ; Ridout, D (ELSEVIER SCIENCE BV, 20070319)

ItemThe extended algebra of the minimal modelsMathieu, P ; Ridout, D (ELSEVIER, 20070806)

ItemFrom percolation to logarithmic conformal field theoryMathieu, P ; Ridout, D (ELSEVIER, 20071129)

ItemLogarithmic M(2, p) minimal models, their logarithmic couplings, and dualityMathieu, P ; Ridout, D (ELSEVIER, 20081001)

ItemOn staggered indecomposable Virasoro modulesKytola, K ; Ridout, D (AMER INST PHYSICS, 200912)In this article, certain indecomposable Virasoro modules are studied. Specifically, the Virasoro mode L0 is assumed to be nondiagonalizable, possessing Jordan blocks of rank 2. Moreover, the module is further assumed to have a highest weight submodule, the “left module,” and that the quotient by this submodule yields another highest weight module, the “right module.” Such modules, which have been called staggered, have appeared repeatedly in the logarithmic conformal field theory literature, but their theory has not been explored in full generality. Here, such a theory is developed for the Virasoro algebra using rather elementary techniques. The focus centers on two different but related questions typically encountered in practical studies: How can one identify a given staggered module, and how can one demonstrate the existence of a proposed staggered module. Given just the values of the highest weights of the left and right modules, themselves subject to simple necessary conditions, invariants are defined which together with the knowledge of the left and right modules uniquely identify a staggered module. The possible values of these invariants form a vector space of dimension 0, 1, or 2, and the structures of the left and right modules limit the isomorphism classes of the corresponding staggered modules to an affine subspace (possibly empty). The number of invariants and affine restrictions is purely determined by the structures of the left and right modules. Moreover, in order to facilitate applications, the expressions for the invariants and restrictions are given by formulas as explicit as possible (they generally rely on expressions for Virasoro singular vectors). Finally, the text is liberally peppered throughout with examples illustrating the general concepts. These have been carefully chosen for their physical relevance or for the novel features they exhibit.