Domain Walls in Strongly Coupled Theories

Domain walls in strongly coupled gauge theories are discussed. A general mechanism is suggested automatically leading to massless gauge bosons localized on the wall. In one of the models considered, outside the wall the theory is in the non-Abelian confining phase, while inside the wall it is in the Abelian Coulomb phase. Confining property of the non-Abelian theories is a key ingredient of the mechanism which may be of practical use in the context of the dynamic compactification scenarios. In supersymmetric (N=1) Yang-Mills theories the energy density of the wall can be exactly calculated in the strong coupling regime. This calculation presents a further example of non-trivial physical quantities that can be found exactly by exploiting specific properties of supersymmetry. A key observation is the fact that the wall in this theory is a BPS-saturated state.Comment: Several typos correcte

Top quark longitudinal polarization near the threshold in l+ l- annihilation

We show that the longitudinal polarization of the top quarks produced in the annihilation of e+ e- or mu+ mu- into tbar t at energies near the threshold is not affected by the large Coulomb-type corrections, which greatly modify the total cross section. Thus the longitudinal polarization, although small, may provide an independent information on the mass and the width of the top quark, largely independent of the uncertainty in alpha_s.Comment: 6 pages, LaTeX, no figures, added references, corrected typo

Operator Product Expansion, Heavy Quarks, QCD Duality and its Violations

The quark (gluon)-hadron duality constitutes a basis for the theoretical treatment of a wide range of inclusive processes -- from hadronic \tau decays and R_{e^+e^-}, to semileptonic and nonleptonic decay rates of heavy flavor hadrons. A theoretical analysis of these processes is carried out by using the operator product expansion in the Euclidean domain, with subsequent analytic continuation to the Minkowski domain. We formulate the notion of the quark (gluon)-hadron duality in quantitative terms, then classify various contributions leading to violations of duality. A prominent role in the violations of duality seems to belong to the so called exponential terms which, conceptually, may represent the (truncated) tail of the power series. A qualitative model, relying on an instanton background field, is developed, allowing one to get an estimate of the exponential terms. We then discuss a number of applications, mostly from heavy quark physics.Comment: 59 pages, 6 figures, epsf.sty required. Revised: Styllistic changes; minor clarifications added; three references corrected; minor changes in the color-related factor

On domain shapes and processes in supersymmetric theories

A supersymmetric theory with several scalar superfields generically has several domain wall type classical configurations which interpolate between various supersymmetric vacua of the scalar fields. Depending on the couplings, some of these configurations develop instability and decay into multiple domain walls, others can form intersections in space. These phenomena are considered here in a simplest, yet non-trivial, model with two scalar superfields.Comment: 10 pages, LaTeX, 5 figures in LaTe

Modified mode-expansion on a BPS wall related to the nonlinear realization

We propose a modified mode-expansion of the bulk fields in a BPS domain wall background to obtain the effective theory on the wall. The broken SUSY is nonlinearly realized on each mode defined by our mode-expansion. Our work clarifies a relation between two different approaches to derive the effective theory on a BPS wall, {\it i.e.} the nonlinear realization approach and the mode-expansion approach. We also discuss a further modification that respects the Lorentz and $U(1)_R$ symmetries broken by the wall.Comment: LaTeX file, 21 pages, no figure

Domain walls in supersymmetric QCD: from weak to strong coupling

We consider domain walls that appear in supersymmetric QCD with Nf < Nc massive flavours. In particular, for 2 Nf < Nc we explicitly construct the domain walls that interpolate between vacua labeled by i and (i+ N_f). We show that these solutions are Bogomol'nyi-Prasad-Sommerfield (BPS) saturated for any value of the mass of the matter fields. This fact allows us to evaluate the large mass limit of these domain walls. We comment on the relevance of these solutions for supersymmetric gluodynamics.Comment: 4 pages, 4 figures, LaTex, uses psfig.st

N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R, Q_R}. These central charges have no parallels, and they can exist only in two dimensions. The central extension of the N=2 superalgebra we found paves the way to a novel phenomenon -- spontaneous breaking of a part of supersymmetry. In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum energy density is positive), while the remaining 1/2 is realized linearly. In the model at hand the standard fermion number is not defined, so that the Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are useless. We show how to construct an index for counting short multiplets in internal algebraic terms which is well-defined in spite of the absence of the standard fermion number. Finally, we outline derivation of the quantum anomaly in {\bar Q_L, Q_R}.Comment: 21 pages, Latex, 1 eps figure. Two important references adde