The essence of the chiral magnetic effect is generation of an electric current along an external magnetic field. Recently it has been studied by Rebhan, Schmitt, and Stricker within the Sakai-Sugimoto model, where it was shown to be zero. As an alternative, we calculate the chiral magnetic effect in soft-wall AdS/ QCD and find a nonzero result with the natural boundary conditions. The mechanism of the dynamical neutralization of the chiral chemical potential via the string production is discussed in the dual two-form representation.

Chiral condensate and η ′ 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 an analytic (quadratic) dependence of condensate on field, typical for the Nambu-Jona-Lasinio model, rather than the nonanalytic (linear in field) result, typical for chiral perturbation theory in the exact chiral limit. We conjecture that the analytic (quadratic) result might be put into correspondence with the leading-order in the 1/N c decomposition for the condensate. This leading order in the 1/N c approximation has not yet been derived from the chiral perturbation theory. Thus the dual model yields the quadratic field dependence of the condensate, which is beyond the range of feasibility of chiral perturbation theory.

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.Effectiveness of the new Model is illustrated by the example of Υ(1S) decay where the standard analysis gives α s (M Υ ) = 0.170 ± 0.004 value that is inconsistent with the bulk of data for α s . Instead, we obtain α M od s (M Υ ) = 0.185 ± 0.005 that corresponds to α M od s (M Z ) = 0.120 ± 0.002 that is close to the world average. The issue of scale uncertainty for Υ decay is also discussed.Later on, both the constructions were joined [9] by suitable integral transformations into the so-called Analytic Perturbation Theory (APT). An essential feature of the APT scheme is that Minkowskian and Euclidean counterparts for powers of usual QCD coupling (α s (Q 2 )) k form nonpower sets {A k (s)} and {A k (Q 2 )} . For the fresh reviews of APT see [10,11].Meanwhile, ghost free APT expressions for effective couplings in the Euclidean α E (Q 2 ) and Minkowskian α M (s) regions, as well as for their "effective powers" A k (Q 2 ) and A k (s), are presented by simple analytic expressions only in the one-loop case (see eqs.(6)-(9)), which are not accurate enough for practical goals.Higher-loop APT expressions are more intricate involving a special Lambert function. A few years ago the first three of them A k (Q 2 ) , A k (s); (k = 1, 2, 3) , sufficient for most of applications, were tabulated by Magradze and Kourashev [12] in the 3-loop case.Here, we propose simple model expressions for 3-loop APT couplings α E (Q 2 ) = A 1 , α M (s) = A 1 and for higher expansion functions A k (Q 2 ) , A k (s) connected by simple iterative relations. The Model depends on one additional parameter and is valid in the region above 1 GeV .The paper is organized as follows. Sections 1 and 2 contain a brief review of the main ideas, technique and some results of APT. In Section 3, we present our Model. Section 4 contains revised analysis of Υ decay data with α s value extracted anew by means of APT and our Model. Special attention is paid to scale uncertainty. The last, Section 5, is devoted to the summary of the results.

The agreement between string theory and field theory is demonstrated in the leading order by providing the first calculation of the correlator of three two-impurity BMN states with all non-zero momenta. The calculation is performed in two completely independent ways: in field theory by using the large-N perturbative expansion, up to the terms subleading in finite-size, and in string theory by using the Dobashi-Yoneya 3-string vertex in the leading order of the Penrose expansion. The two results come out to be completely identical.