The extended conformal theory of the Calogero-Sutherland model

We describe the recently introduced method of Algebraic Bosonization of (1+1)-dimensional fermionic systems by discussing the specific case of the Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also presented.Comment: 12 pages, plain LaTeX, no figures; To appear in the proceedings of the IV Meeting "Common Trends in Condensed Matter and High Energy Physics", Chia Laguna, Cagliari, Italy, 3-10 Sep. 199

The extended conformal theory of Luttinger systems

We describe the recently introduced method of algebraic bosonization of the $(1+1)$-dimensional Luttinger systems by discussing in detail the specific case of the Calogero-Sutherland model, and mentioning the hard-core Bose gas. We also compare our findings with the exact Bethe Ansatz results.Comment: 9 pages, plain Latex file, ,based on a talk given by S. Sciuto at the II International Sakharov Conference on Physics, Moscow, Russia, 20-24 May 9

Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

We propose an approach to treat (1+1)--dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decompose the elementary low-lying excitations around the Fermi surface in terms of basic building blocks which carry a representation of the W_{1+\infty} \times {\overline W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum incompressible fluid. This symmetry simply expresses the local particle-number current conservation at the Fermi surface. The general approach is illustrated in detail in two examples: the Heisenberg and Calogero-Sutherland models, which allow for a comparison with the exact Bethe Ansatz solution.Comment: 51 pages, plain LaTe

Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)})

We give a realization of the quantum affine Lie superalgebras U_q(A(M,N))^(1) in terms of anyons defined on a one or two-dimensional lattice, the deformation parameter q being related to the statistical parameter $\nu$ of the anyons by q = exp(i\pi\nu). The construction uses anyons contructed from usual fermionic oscillators and deformed bosonic oscillators. As a byproduct, realization deformed in any sector of the quantum superalgebras U_q(A(M,N)) is obtained.Comment: 14p LaTeX Document (should be run twice

Non-perturbative studies of N=2 conformal quiver gauge theories

We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n=1,2, also in the presence of an Omega-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotential a la Nekrasov using localization methods.Comment: 56 pages, 7 figures, PdfLaTeX. v2: a few references added, version to appear on Fortschritte der Physi

Modular and duality properties of surface operators in N=2* gauge theories

We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure N=2 or to N=2* gauge theories.Comment: 51 pages, v3: references added, typos fixed, footnote added, some small changes in the text, appendix B streamlined. Matches the published versio

On the Fock space for nonrelativistic anyon fields and braided tensor products

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the 1-particle Hilbert space. This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category. We see how essential physical information is thus encoded. In particular we show how the algebraic structure of our anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealised gas of fixed anyonic vortices.Comment: Added some references, more explicit formulae for the discrete case and remark on partition function. 25 pages latex, no figure

The abandoned antimony-mines of SE Sardinia: impact on surface waters

This study investigates the impact of abandoned Sb-mines on the Flumendosa River, which is the most important water resource in southern Sardinia. Hydrogeochemical surveys carried out in 2005 and 2006 indicated a significant impact of waters flowing out from adits, slag, tailings and waste materials on surface waters. The contaminated waters show alkaline pH, and high dissolved SO4, Sb and As (up to 1900, 9.6 and 3.5 mg/L, respectively). Although the flow rates of drainages from the mining area are usually low (in the range of < 0.1 to 1 L/s), the contribution to dissolved concentrations of Sb in the streams downstream of mines is high. Sampling under high flow conditions in the Flumendosa River before the confluence with the contaminated streams showed Sb concentrations below the limits established by the guidelines of World Health Organization for drinking water (i.e. 20 g/L), while downstream of the confluence dissolved Sb was 32 g/L. Contamination in the Flumendosa extended 16 km, and attenuation (15 g/L Sb) was only observed close to the Flumendosa mouth

Surface operators in 5d gauge theories and duality relations

We study half-BPS surface operators in 5d N=1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.Comment: 39 pages. v2: A few sentences rephrased, references added, and typos corrected. Matches version published in JHE