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

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

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

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

Analytic Perturbation Theory for Practitioners and Upsilon Decay

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and time-like (Minkowskian) regions, accurate enough in the large range (1--100 GeV) of current physical interest.\par Effectiveness of the new Model is illustrated by the example of $\Upsilon(1\mathrm{S})$ decay where the standard analysis gives $\alpha_s(M_{\Upsilon})=0.170\pm 0.004$ value that is inconsistent with the bulk of data for $\alpha_s$. Instead, we obtain $\alpha_s^{Mod}(M_{\Upsilon})=0.185\pm 0.005$ that corresponds to $\alpha_s^{Mod}(M_Z)=0.120\pm 0.002$ that is close to the world average.\par The issue of scale uncertainty for $\Upsilon$ decay is also discussed.Comment: 12 pages, 0 figures. Model slightly modified to increase its accuracy. Numerical results upgraded, references added. The issue of scale uncertainty is discusse

Anomalous Zero Sound

We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.Comment: 14 pages, 2 figure