Morse Theory in Field Theory

We describe correlations functions of topological quantum mechanics (TQM) in terms of Morse theory. We review the basics of topological field theories and discuss geometric and algebraic interpretations of TQM. We prove that correlators in TQM can be expressed via intersection numbers of certain submanifolds of the target space with paths of steepest descent between critical points of a Morse function. In the end we conjecture another correspondence between quantum mechanics correlators and integrals of Massey products of certain cohomology classes.Comment: updated versio

Monopole Decay in a Variable External Field

The rate of monopole decay into a dyon and an electron in an inhomogeneous external electric field is calculated by semiclassical methods. Comparison is made to an earlier result where this quantity was calculated for a constant field. Experimental and cosmological tests are suggested.Comment: 15 pages, 8 figures. v2: typos removed, list of references update

QCD Vacuum Properties in a Magnetic Field from AdS/CFT: Chiral Condensate and Goldstone Mass

Chiral condensate and $\eta^\prime$ meson mass spectrum are studied under the influence of an external Abelian magnetic field. We work within the D3/D7 Karch--Katz model of flavoured AdS/CFT with supersymmetry broken by the Constable--Myers deformation of the metric. It is shown that this setting yields a quadratic dependence of condensate on field, rather than the non-analytic (linear in field) dependence, typical for chiral perturbation theory in the exact chiral limit. We argue that the analytic (quadratic) result must be put into correspondence with the leading-order in the $1/N_c$ decomposition for the condensate, whereas the existing chiral perturbation theory result, which is linear in field strength, is $1/N_c$ suppressed.Comment: 11 pages, 5 figure

Stabilization of Self-slaking Slags from Ferroalloy Production

In this study, the process of stabilization for highly basic self-slaking slags of ferroalloy production by various boron-containing materials were studied: tincalconite, colemanite, and ulexite (produced in Turkey). The viscosities and temperatures of crystallization for the initial boron-containing materials are determined. Under laboratory conditions, high-base slag melts were treated with boron-containing materials to obtain slags containing 0.25 and 0.5% B2О3. It was shown that the addition of boric anhydride to the studied slag melts extends the homogeneous-liquid state interval and reduces their viscosity by 1.2–1.6 times, therefore B2О3can be used as a tool for controlling slag mobility in industrial conditions. The industrial tests were conducted to stabilize the slag of low-carbon ferrochrome using powdered calcined, briquetted, and fused colemanite. After treatment, slags contained 43–47% CaO, 0.18–0.45% B2О3. The results of pilot-industrial experiments show that all applied boron-containing materials ensure slag stabilization and differ only in the degree of boron recovery. Fused colemanite showed the highest results in the recovery of B2О3(up to 98%), a commercial product was obtained which fully complies according to the technical characteristics with the requirements of Specification TU 0798-69-00186499-2014 “Crushed stone and sand from ferroalloy slags. Technical conditions.” Keywords: ferroalloy, slag, self-slaking slag, stabilization, boron, two-calcium silicat

The Confinement Property in SU(3) Gauge Theory

We study confinement property of pure SU(3) gauge theory, combining in this effort the non-perturbative gluon and ghost propagators obtained as solutions of Dyson--Schwinger equations with solutions of an integral ladder diagram summation type equation for the Wilson loop. We obtain the string potential and effective UV coupling.Comment: 7 pages, 7 figures, v2: references added, discussion reorganize