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

Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N_f flavors of massive quarks deformed by the mass term \mu for the adjoint matter, W=\mu A^2, assuming that N\leq N_f<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small \mu, so that the Z_N strings preserve, in a sense, their BPS nature. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N_f-1) model on the string world sheet. The bulk \mu-deformation makes this theory N= (0,2) supersymmetric heterotic weighted CP(N_f-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.Comment: 39 pages, 1 fig; v2: 1 reference added, two explanatory remarks added; Final version, to appear in PR

Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality

The crossover transition from weak coupling at large \xi to strong coupling at small \xi is studied in N=2 supersymmetric gauge theory with the U(N) gauge group and N_f>N (here \xi is the Fayet--Iliopoulos parameter). We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small \xi. The dual gauge group is U(N_f-N). The dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both theories support non-Abelian strings. In each of these two regimes there are two varieties of physical excitations: elementary fields and nonperturbative composite states bound by confining strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields.Comment: Plenary talk at SUSY09: 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions, Northeastern Univ. Boston, 5-10 June, 200