Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if the weight semigroup of G/H satisfies some simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction

Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives

Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, is obtained using Schwinger-Dyson equations and Slavnov-Tailor identities. A possible deviation of the result from the corresponding contribution in the exact Novikov, Shifman, Vainshtein and Zakharov $\beta$-function is discussed.Comment: 20 pages, 4 figure

Crystal Chemistry of Carbon-Substituted MgB2

Neutron powder diffraction has been used to characterize a sample of C-substituted MgB2 synthesized from Mg and B4C (with isotopically enriched 11B). The sample is multiphase, with the major phase [73.4(1) wt.%] being Mg(B1-xCx)2 with x=0.10(2). Minor phases include MgB2C2, Mg, and MgO. The major Mg(B1-xCx)2 phase displays diffraction peak widths as sharp as for pure MgB2, indicating good C homogeneity. There is no evidence for ordering of the substituted C atoms or distortion of the host structure other than contraction of the a axis and slight expansion of the c axis. The observed changes in lattice parameters vs. C concentration provide a means for estimating the C concentration in other Mg(B1-xCx)2 samples. The reduction in Tc resulting from 10% C substitution is much larger than previously reported, suggesting that previous reports of the C concentration in Mg(B1-xCx)2 are overestimated. The Mg site occupancy is determined to be 0.990(4) which is consistent with full Mg occupancy. Given these results, the stoichiometry Mg(B0.9C0.1)2 should be used by future attempts (band structural or otherwise) to explain (i) the dramatic suppression of Tc (Tc ~ = 22 K) and (ii) the persistence of the two-superconducting-gap feature in the specific heat data.Comment: 14 pages, 3 figure

The Four-Loop Konishi in N=4 SYM

We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield (arXiv:0712.3522, arXiv:0806.2095) and superstring (arXiv:0807.0399) computations, which take into account finite size corrections to the all-loop asymptotic Bethe ansatz for the integrable models describing the spectrum of the anomalous dimensions of the gauge-invariant operators and the spectrum of the string states in the framework of the gauge/string duality.Comment: 7 pages, some detailes of calculations adde

Harmonic analysis on spherical homogeneous spaces with solvable stabilizer

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over G/H.Comment: v2: 14 pages, minor correction

Supersymmetric States in Large N Chern-Simons-Matter Theories

In this paper we study the spectrum of BPS operators/states in N=2 superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N=2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter.Comment: 53 pages, 18 figures. v2: improved numerics, additional comments adde

Special case of sunset: reduction and epsilon-expansion

We consider two loop sunset diagrams with two mass scales m and M at the threshold and pseudotreshold that cannot be treated by earlier published formula. The complete reduction to master integrals is given. The master integrals are evaluated as series in ratio m/M and in epsilon with the help of differential equation method. The rules of asymptotic expansion in the case when q^2 is at the (pseudo)threshold are given.Comment: LaTeX, 13 pages, 1 figur

Towards proof of new identity for Green functions in N=1 supersymmetric electrodynamics

For the N=1 supersymmetric massless electrodynamics, regularized by higher derivatives, we describe a method, by which one can try to prove the new identity for the Green functions, which was proposed earlier. Using this method we show that some contribution to the new identity are really 0.Comment: 16 pages, 1 figure, an error corrected, significant change