Hilbert Schemes, Separated Variables, and D-Branes

We explain Sklyanin's separation of variables in geometrical terms and construct it for Hitchin and Mukai integrable systems. We construct Hilbert schemes of points on $T^{*}\Sigma$ for \Sigma = {\IC}, {\IC}^{*} or elliptic curve, and on ${\bf C}^{2}/{\Gamma}$ and show that their complex deformations are integrable systems of Calogero-Sutherland-Moser type. We present the hyperk\"ahler quotient constructions for Hilbert schemes of points on cotangent bundles to the higher genus curves, utilizing the results of Hurtubise, Kronheimer and Nakajima. Finally we discuss the connections to physics of $D$-branes and string duality.Comment: harvmac, 27 pp. big mode; v2. typos and references correcte

Duality in Integrable Systems and Gauge Theories

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as allow to construct new ones, double elliptic among them. We also discuss applications to the (supersymmetric) gauge theories in various dimensions.Comment: harvmac 45 pp.; v4. minor corrections, to appear in JHE

Electronic Structure of New LiFeAs High-Tc Superconductor

We present results of it ab initio LDA calculations of electronic structure of "next generation" layered ironpnictide High-Tc superconductor LiFeAs (Tc=18K). Obtained electronic structure of LiFeAs is very similar to recently studied ReOFeAs (Re=La,Ce,Pr,Nd,Sm) and AFe2As2 (A=Ba,Sr) compounds. Namely close to the Fermi level its electronic properties are also determined ma inly by Fe 3d-orbitals of FeAs4 two-dimensional layers. Band dispersions of LiFeAs are very similar to the LaOFeAs and BaFe2As2 systems as well as the shape of the Fe-3d density o f states and Fermi surface.Comment: 4 pages, 5 figures; Electronic structure improved with respect to new experimental crystal structure dat

Electronic Structure of New AFFeAs Prototype of Iron Arsenide Superconductors

This work is provoked by recent discovery of new class prototype systems AFFeAs (A=Sr,Ca) of novel layered ironpnictide High-Tc superconductors (Tc=36K). Here we report ab initio LDA results for electronic structure of the AFFeAs systems. We provide detailed comparison between electronic properties of both new systems and reference LaOFeAs (La111) compound. In the vicinity of the Fermi level all three systems have essentially the same band dispersions. However for iron fluoride systems F(2p) states were found to be separated in energy from As(4p) ones in contrast to La111, where O(2p) states strongly overlaps with As(4p). Thus it should be more plausible to include only Fe(3d) and As(4p) orbitals into a realistic noninteracting model than for La111. Moreover Sr substitution with smaller ionic radius Ca in AFFeAs materials leads to a lattice contruction and stronger Fe(3d)-As(4p) hybridization resulting in smaller value of the density of states at the Fermi level in the case of Ca compound. So to some extend Ca system reminds RE111 with later Rare Earths. However Fermi surface of new fluorides is found to be nearly perfect two-dimensional. Also we do not expect strong dependence of superconducting properties with respect to different types of A substitutes.Comment: 5 pages, 4 figure