Instanton Dynamics in the Broken Phase of the Topological Sigma Model

The topological $\sigma$ model with the black hole metric of the target space is considered. It has been shown before that this model is in the phase with BRST-symmetry broken. In particular, vacuum energy is non-\-zero and correlation functions of observables show the coordinate dependence. However these quantities turned out to be infrared (IR) divergent. It is shown here that IR divergences disappear after the sum over an arbitrary number of additional instanton-\-anti-\-instanton pairs is performed. The model appears to be equivalent to Coulomb gas/Sine Gordon system.Comment: some references added

The Broken Phase of the Topological Sigma model

The topological sigma model with the semi-infinite cigar-like target space (black hole geometry) is considered. The model is shown to possess unsuppressed instantons. The noncompactness of the moduli space of these instantons is responsible for an unusual physics. There is a stable vacuum state in which the vacuum energy is zero, correlation functions are numbers thus the model is in the topological phase. However, there are other vacuum states in which correlation functions show the coordinate dependence. The estimation of the vacuum energy indicates that it is nonzero. These states are interpreted as the ones with broken BRST-symmetry.Comment: 30 pages, LATE

The Higgs and Coulomb/Confining Phases in "Twisted-Mass" Deformed CP(N-1) Model

We consider non-supersymmetric two-dimensional CP(N-1) model deformed by a term presenting the bosonic part of the twisted mass deformation of N=2 supersymmetric version of the model. Our deformation has a special form preserving a Z_N symmetry at the Lagrangian level. In the large mass limit the model is weakly coupled. Its dynamics is described by the Higgs phase, with Z_N spontaneously broken. At small masses it is in the strong coupling Coulomb/confining phase. The Z_N symmetry is restored. Two phases are separated by a phase transition. We find the phase transition point in the large-N limit. It lies at strong coupling. As was expected, the phase transition is related to broken versus unbroken Z_N symmetry in these two respective phases. The vacuum energies for these phases are determined too.Comment: 20 pages, 3 figures, reference adde

Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies

By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as particular cases. We develop the generalized graded R-matrix formalism using the generalized graded bracket on the space of graded operators with involution generalizing the graded commutator in superalgebras, which allows one to describe these hierarchies in the framework of the Hamiltonian formalism and construct their first two Hamiltonian structures. The first Hamiltonian structure is obtained for both bosonic and fermionic Lax operators while the second Hamiltonian structure is established for bosonic Lax operators only.Comment: 12 pages, LaTeX, the talks delivered at the International Workshop on Classical and Quantum Integrable Systems (Dubna, January 24 - 28, 2005) and International Conference on Theoretical Physics (Moscow, April 11 - 16, 2005

The structure of the exact effective action and the quark confinement in MSSM QCD

An expression for the exact (nonperturbative) effective action of $N$=1 supersymmetric gauge theories is proposed, supposing, that all particles except for the gauge bosons are massive. Analysis of its form shows, that instanton effects in the supersymmetric theories can lead to the quark confinement. The typical scale of confinement in MSSM QCD, calculated from the first principles, is in agreement with the experimental data. The proposed explanation is quite different from the dual Higgs mechanism.Comment: Final version to appear in Sov.J.Nucl.Phys. Some insignificant errors and misprints are correcte

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in J.Phys.A (Fast Track Communication