On the Chiral WZNW Phase Space, Exchange r-Matrices and Poisson-Lie Groupoids

This is a review of recent work on the chiral extensions of the WZNW phase space describing both the extensions based on fields with generic monodromy as well as those using Bloch waves with diagonal monodromy. The symplectic form on the extended phase space is inverted in both cases and the chiral WZNW fields are found to satisfy quadratic Poisson bracket relations characterized by monodromy dependent exchange r-matrices. Explicit expressions for the exchange r-matrices in terms of the arbitrary monodromy dependent 2-form appearing in the chiral WZNW symplectic form are given. The exchange r-matrices in the general case are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group $G$, exchange r-matrices are exhibited that are in one-to-one correspondence with the possible PL structures on $G$ and admit them as PL symmetries.Comment: Based on a lecture by L.F. at the Seminaire de Mathematiques Superieures, Montreal, 1999; LaTeX, 21 page

A2 Toda theory in reduced WZNW framework and the representations of the W algebra

Using the reduced WZNW formulation we analyse the classical $W$ orbit content of the space of classical solutions of the $A_2$ Toda theory. We define the quantized Toda field as a periodic primary field of the $W$ algebra satisfying the quantized equations of motion. We show that this local operator can be constructed consistently only in a Hilbert space consisting of the representations corresponding to the minimal models of the $W$ algebra.Comment: 38 page

Multifractal Network Generator

We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed statistical properties, e.g., with degree- or clustering coefficient distributions of various, very different forms. In turn, these graphs can be used to test hypotheses, or, as models of actual data. The method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks. Such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies. The main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously. A very unique feature of this construction is that the complexity of the generated network is increasing with the size. We present analytic expressions derived from the parameters of the -- to be iterated-- initial generating measure for such major characteristics of graphs as their degree, clustering coefficient and assortativity coefficient distributions. The optimal parameters of the generating measure are determined from a simple simulated annealing process. Thus, the present work provides a tool for researchers from a variety of fields (such as biology, computer science, biology, or complex systems) enabling them to create a versatile model of their network data.Comment: Preprint. Final version appeared in PNAS

Quantum corrections of Abelian Duality Transformations

A modification of the Abelian Duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) $\sigma$-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat non standard perturbative treatment of the {\sl dual} $\sigma$-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric $\sigma$-models.Comment: Latex 11 pages; remarks on a free model and references adde

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi Witten string in the light cone gauge are reviewed.Comment: 21 pages, Plain Tex, to appear in the E.P. Wigner memorial volume of Acta Physica Hungaric

Post-T Tauri stars: a false problem

We consider the problem of the apparent lack of old T Tauri stars in low-mass star forming regions in the framework of the standard model of low-mass star formation. We argue that the similarity between molecular cloud lifetime and ambipolar diffusion timescale implies that star formation does not take place instantaneously, nor at a constant rate. We conclude that the probability of finding a large population of old stars in a star forming region is intrinsically very small and that the post-T Tauri problem is by and large not existent.Comment: 6 pages (LaTeX), no Figures to be published in The Astrophysical Journal Letter

Response to “Comment on ‘Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles”’ [J. Chem. Phys. 138, 157101 (2013)]

No abstract: this is a "response" to a Comment