[en] The free fields on a Riemann surface carrying spin structures live on an unramified r-covering of the surface itself. When the surface is represented as an algebraic curve related to the vanishing of the Weierstrass polynomial, its r-coverings are algebraic curves as well. We construct explicitly the Weierstrass polynomial associated to the r-coverings of an algebraic curve. Using standard techniques of algebraic geometry it is then possible to solve the inverse Jacobi problem for the odd spin structures. As an application we derive the partition functions of bosonic string theories in many examples, including two general curves of genus three and four. The partition functions are explicitly expressed in terms of branch points apart from a factor which is essentially a theta constant. 53 refs., 4 figs. (Author)

[en] In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simble b-c systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides the fact that one obtains in this way an entire class of theories in which the operators obey nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case. (orig.)

[en] Forward osmosis (FO) is a promising technology for wastewater (WW) treatment due to its lower energy requirements, higher permeate purity and lower fouling. Applying FO directly on raw municipal WW is of high interest to simultaneously produce a high quality permeate for water reuse while pre-concentrating wastewater for anaerobic digestion towards energy and nutrients recovery. This bench scale study investigated the feasibility to concentrate real raw municipal WW using FO to reach 70% water recovery with a home-made submerged plate and frame membrane module, assembled using Toray’s flat-sheet TFC membrane. Process showed high COD rejection and high differences in ion rejection depending on the charge (SO4 2-=99±2%, PO4 3--=99±2%, NH4 +=17±4%, Ca2+=10±2%). Three different gas sparging strategies (continuous air sparging, alternating nitrogen sparging and no gas sparging) were tested to control membrane fouling, being the continuous air sparging the most favorable.

[en] We discuss here exotic conformal field theories associated with the b-c systems on a class of algebraic curves with nonabelian symmetry group. In particular we derive explicitly the primary fields of these conformal field theories and their operator product expansions. The braiding relations between the primary fields show that they satisfy a nontrivial exotic statistics. (orig.)

[en] It is shown that all the (p,q) dyon bound states exist and are unique in N=4 and N=2 with four massless flavor supersymmetric SU(2) Yang-Mills theories, where p and q are any relatively prime integers. The proof can be understood in the context of field theory alone, and does not rely on any duality assumption. We also give a general physical argument showing that these theories should have at least an exact Γ(2) duality symmetry, and then deduce in particular the existence of the (2p,2q) vector multiplets in the N_f=4 theory. The corresponding massive theories are studied in parallel, and it is shown that though in these cases the spectrum is no longer self-dual at a given point on the moduli space, it is still in perfect agreement with an exact S duality. We also discuss the interplay between our results and both the semiclassical quantization and the heterotic-type II string-string duality conjecture. (orig.)

[en] We consider here the Chern-Simons field theory with the gauge group SU(N) in the presence of a conformally flat gravitational background that describes a two-dimensional expanding ''universe.'' The propagator and the vertices are explicitly computed at the second order in perturbation theory imposing the Coulomb gauge fixing. It is shown in this gauge that the correlation functions of the gauge fields are independent of the metric

[en] In this Letter, the correlation functions of the free fermions with odd spin structures are derived on a general hyperelliptic curve. In order to express the correlators explicitly in terms of the branch points, we construct the analogous of the Szegoe kernel for the odd spin structures. (orig.)

[en] Some non-perturbative aspects of non-Abelian four dimensional space-time gauge theories are presented. Precise results were obtained in the frame of supersymmetric theories pointing out the resulting physics related to strong coupling gauge field dynamics

[en] I review, with some pedagogy, two different approaches to the computation of BPS spectra in N = 2 supersymmetric QCD with gauge group SU(2). The first one is semiclassical and has been widely used in the literature. The second one makes use of constraints coming from the non perturbative, global structure of the Coulomb branch of these theories. The second method allows for a description of discontinuities in the BPS spectra at strong coupling, and should lead to accurate test of duality conjectures in N = 2 theories. (orig.)

[en] We present a detailed study of the analytic structure, BPS spectra and superconformal points of the N=2 susy SU(2) gauge theories with N_f=1,2,3 massive quark hypermultiplets. We compute the curves of marginal stability with the help of the explicit solutions for the low-energy effective actions in terms of standard elliptic functions. We show that only a few of these curves are relevant. As a generic example, the case of N_f=2 with two equal bare masses is studied in depth. We determine the precise existence domains for each BPS state, and show how they are compatible with the RG flows. At the superconformal point, where two singularities coincide, we prove that (for N_f=2) the massless spectrum consists of four distinct BPS states and is S-invariant. This is due to the monodromy around the superconformal point being S, providing strong evidence for exact S-duality of the SCFT. For all N_f, we compute the slopes ω of the β-functions at the fixed point couplings and show that they are related to the anomalous dimensions α of u= left angle tr φ² right angle by ω=2(α-1). (orig.)