Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.Comment: 4 pages, 4 figures, typos correcte

Conformal Moduli and b-c Pictures for NSR Strings

We explore the geometry of the superconformal moduli of the NSR superstring theory in order to construct the consistent sigma-model for the NSR strings, free of picture-changing ambiguities. The sigma-model generating functional is constructed by the integration over the bosonic and anticommuting moduli, corresponding to insertions of the vertex operators in scattering amplitudes. In particular, the integration over the bosonic moduli results in the appearance of picture-changing operators for the b-c system. Important example of the b-c pictures involves the unintegrated and integrated forms of the vertex operators. We derive the BRST-invariant expressions for the b-c picture-changing operators for open and closed strings and study some of their properties. We also show that the superconformal moduli spaces of the NSR superstring theory contain the global singularities, leading to the appearance of non-perturbative solitonic D-brane creation operators.Comment: 22 pages, references adde

Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD

We consider a benchmark bulk theory in four-dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of fundamental matter hypermultiplets (quarks). The nature of the BPS strings in this benchmark theory crucially depends on N_f. If N_f\geq N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N_f>N these strings become semilocal, developing additional moduli \rho related to (unlimited) variations of their transverse size. Using the U(2) gauge group with N_f=3,4 as an example, we derive an effective low-energy theory on the (two-dimensional) string world sheet. Our derivation is field-theoretic, direct and explicit: we first analyze the Bogomol'nyi equations for string-geometry solitons, suggest an ansatz and solve it at large \rho. Then we use this solution to obtain the world-sheet theory. In the semiclassical limit our result confirms the Hanany-Tong conjecture, which rests on brane-based arguments, that the world-sheet theory is N=2 supersymmetric U(1) gauge theory with N positively and N_e=N_f-N negatively charged matter multiplets and the Fayet-Iliopoulos term determined by the four-dimensional coupling constant. We conclude that the Higgs branch of this model is not lifted by quantum effects. As a result, such strings cannot confine. Our analysis of infrared effects, not seen in the Hanany-Tong consideration, shows that, in fact, the derivative expansion can make sense only provided the theory under consideration is regularized in the infrared, e.g. by the quark mass differences. The world-sheet action discussed in this paper becomes a bona fide low-energy effective action only if \Delta m_{AB}\neq 0.Comment: 36 pages, no figure

Magnetic strings in Lattice QCD as Nonabelian Vortices

Lattice studies indicate existence of magnetic strings in QCD vacuum. We argue that recently found nonabelian strings with rich worldsheet dynamics provide a proper pattern for the strings observed on the lattice. In particular, within this pattern we explain the localization of the monopole-antimonopole pairs on the magnetic string worldsheet and the negative contribution of the magnetic strings into the vacuum energy and gluon condensate. We suggest the D2 brane realization of the magnetic string which explains the temperature dependence of its tension.Comment: 17 pages, 1 figur

On the issue of public-private partnership in housing construction in the Belgorod region

The article discusses the opportunities and prospects for the use of public-private partnership (PPP) tools for the implementation of investment projects in housing construction in the Belgorod region. The application of the PPP concept will allow to attract additional investment resources to the region, will provide an opportunity to strengthen its competitive advantages and unleash innovative potentia

Baxter Equation for the QCD Odderon

The Hamiltonian derived by Bartels, Kwiecinski and Praszalowicz for the study of high-energy QCD in the generalized logarithmic approximation was found to correspond to the Hamiltonian of an integrable $XXX$ spin chain. We study the odderon Hamiltonian corresponding to three sites by means of the Bethe Ansatz approach. We rewrite the Baxter equation, and consequently the Bethe Ansatz equations, as a linear triangular system. We derive a new expression for the eigenvectors and the eigenvalues, and discuss the quantization of the conserved quantities.Comment: 14 pages, latex file, one figur

Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism

Although the AdS_5xS^5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS_5xS^5 background than in a flat background. The BRST operator acts geometrically, the left and right-moving pure spinor ghosts can be treated as complex conjugates, the zero mode measure factor is trivial, and the b ghost does not require non-minimal fields. Furthermore, a topological version of the AdS_5xS^5 action with the same worldsheet variables and BRST operator can be constructed by gauge-fixing a G/G principal chiral model where G=PSU(2,2|4). This topological model is argued to describe the zero radius limit that is dual to free N=4 super-Yang-Mills and can also be interpreted as an "unbroken phase" of superstring theory.Comment: 39 pages harvma

On the stability problem in the O(N) nonlinear sigma model

The stability problem for the O(N) nonlinear sigma model in the 2+\epsilon dimensions is considered. We present the results of the 1/N^{2} order calculations of the critical exponents (in the 2<d<4 dimensions) of the composite operators relevant for this problem. The arguments in the favor of the scenario with the conventional fixed point are given.Comment: 9 pages, revtex, 1 Postscript figur

Electromagnetic Interaction in the System of Multimonopoles and Vortex Rings

Behavior of static axially symmetric monopole-antimonopole and vortex ring solutions of the SU(2) Yang-Mills-Higgs theory in an external uniform magnetic field is considered. It is argued that the axially symmetric monopole-antimonopole chains and vortex rings can be treated as a bounded electromagnetic system of the magnetic charges and the electric current rings. The magnitude of the external field is a parameter which may be used to test the structure of the static potential of the effective electromagnetic interaction between the monopoles with opposite orientation in the group space. It is shown that for a non-BPS solutions there is a local minimum of this potential.Comment: 10 pages, 12 figures, some minor corrections, version to appear in Phys. Rev.

Compact QED3 with theta term and axionic confining strings

We discuss three dimensional compact QED with a theta term due to an axionic field. The variational gauge invariant functional is considered and it is shown that the ground state energy is independent of theta in a leading approximation. The mass gap of the axionic field is found to be dependent upon theta, the mass gap of the photon field and the scalar potential. The vacuum expectation of the Wilson loop is shown to be independent of theta in a leading approximation, to obey the area law and to lead to confinement. We also briefly discuss the properties of axionic confining strings.Comment: 35 pages, LaTex, typing error correcte