't Hooft Operators in Gauge Theory from Toda CFT

We construct loop operators in two dimensional Toda CFT and calculate with them the exact expectation value of certain supersymmetric 't Hooft and dyonic loop operators in four dimensional \Ncal=2 gauge theories with SU(N) gauge group. Explicit formulae for 't Hooft and dyonic operators in \Ncal=2^* and \Ncal=2 conformal SQCD with SU(N) gauge group are presented. We also briefly speculate on the Toda CFT realization of arbitrary loop operators in these gauge theories in terms of topological web operators in Toda CFT.Comment: 49 pages, LaTeX. Typos fixed, references adde

Acceleration of generalized hypergeometric functions through precise remainder asymptotics

We express the asymptotics of the remainders of the partial sums {s_n} of the generalized hypergeometric function q+1_F_q through an inverse power series z^n n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k} may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z=1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added several references, added comparison to other methods, and added discussion of recursion stabilit

Simplifying Multiple Sums in Difference Fields

In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package \SigmaP\ by discovering and proving new harmonic number identities extending those from (Paule and Schneider, 2003). In addition, the newly developed package \texttt{EvaluateMultiSums} is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.Comment: Uses svmult.cls, to appear as contribution in the book "Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions" (www.Springer.com

The crystal structure of Cr8O21\mathrm{Cr_8O_{21}} determined from powder diffraction data: Thermal transformation and magnetic properties of a chromium-chromate-tetrachromate

Thermal decomposition of $CrO_3$ was utilized to prepare a powder sample of the chromium oxide usually designated $Cr_3O_8$. Combined information from powder diffraction data using synchrotron, conventional X-ray, and neutron radiation allowed determination of the structure. The structure is triclinic (a = 5.433(1), b = 6.557(1), c = 12.117(2) Å, α = 106.36(1), β = 95.73(1) and γ = 77.96(1)°) and was refined in the space group P1. The true composition of the compound is $Cr_8O_{21}$. There are two distinct types of chromium atoms in the structure, which may be designated the oxidation numbers (III) and (VI), respectively. The structure is built from pairs of edge-sharing Cr(III)O6 octahedra linked together by Cr(VI)O4 tetrahedra to form sheets. The sheets are then linked together by tetrachromate groups ($Cr(VI)_4O_{13}$) to form a three-dimensional structure. Thus, the chromium oxide may be described as $Cr(III)_2(Cr(VI)O_4)_2(Cr(VI)_4O_{13}$). The magnetic properties of $Cr_8O_{21}$ were investigated in the temperature range 5 to 300 K. Above 100 K the compound is paramagnetic. Magnetic susceptibility data indicate a transition to antiferromagnetism around 100 K, but only vague indications for additional magnetic reflections were found with neutron powder diffraction