Revisiting Critical Vortices in Three-Dimensional SQED

We consider renormalization of the central charge and the mass of the ${\cal N}=2$ supersymmetric Abelian vortices in 2+1 dimensions. We obtain ${\cal N}=2$ supersymmetric theory in 2+1 dimensions by dimensionally reducing the ${\cal N}=1$ SQED in 3+1 dimensions with two chiral fields carrying opposite charges. Then we introduce a mass for one of the matter multiplets without breaking N=2 supersymmetry. This massive multiplet is viewed as a regulator in the large mass limit. We show that the mass and the central charge of the vortex get the same nonvanishing quantum corrections, which preserves BPS saturation at the quantum level. Comparison with the operator form of the central extension exhibits fractionalization of a global U(1) charge; it becomes 1/2 for the minimal vortex. The very fact of the mass and charge renormalization is due to a "reflection" of an unbalanced number of the fermion and boson zero modes on the vortex in the regulator sector.Comment: 24 pages, 2 figures Minor modifications, reference adde

Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses

We address a number of unanswered questions in the N=(0,2)-deformed CP(N-1) model with twisted masses. In particular, we complete the program of solving CP(N-1) model with twisted masses in the large-N limit. In hep-th/0512153 nonsupersymmetric version of the model with the Z_N symmetric twisted masses was analyzed in the framework of Witten's method. In arXiv:0803.0698 this analysis was extended: the large-N solution of the heterotic N=(0,2) CP(N-1) model with no twisted masses was found. Here we solve this model with the twisted masses switched on. Dynamical scenarios at large and small m are studied (m is the twisted mass scale). We found three distinct phases and two phase transitions on the m plane. Two phases with the spontaneously broken Z_N-symmetry are separated by a phase with unbroken Z_N. This latter phase is characterized by a unique vacuum and confinement of all U(1) charged fields ("quarks"). In the broken phases (one of them is at strong coupling) there are N degenerate vacua and no confinement, similarly to the situation in the N=(2,2) model. Supersymmetry is spontaneously broken everywhere except a circle |m|=\Lambda in the Z_N-unbroken phase. Related issues are considered. In particular, we discuss the mirror representation for the heterotic model in a certain limiting case.Comment: 69 pages, 14 figures; typos corrected, final version to appear in PRD; v Jan. 2014 Erratum added on p. 50, two references added and two references update

Higher Winding Strings and Confined Monopoles in N=2 SQCD

We consider composite string solutions in N=2 SQCD with the gauge group U(N), the Fayet--Iliopoulos term \xi \neq 0 and N (s)quark flavors. These bulk theories support non-Abelian strings and confined monopoles identified with kinks in the two-dimensional world-sheet theory. Similar and more complicated kinks (corresponding to composite confined monopoles) must exist in the world-sheet theories on composite strings. In a bid to detect them we analyze the Hanany--Tong (HT) model, focusing on a particular example of N=2. Unequal quark mass terms in the bulk theory result in the twisted masses in the N=(2,2) HT model. For spatially coinciding 2-strings, we find three distinct minima of potential energy, corresponding to three different 2-strings. Then we find BPS-saturated kinks interpolating between each pair of vacua. Two kinks can be called elementary. They emanate one unit of the magnetic flux and have the same mass as the conventional 't Hooft--Polyakov monopole on the Coulomb branch of the bulk theory (\xi =0). The third kink represents a composite bimonopole, with twice the minimal magnetic flux. Its mass is twice the mass of the elementary confined monopole. We find instantons in the HT model, and discuss quantum effects in composite strings at strong coupling. In addition, we study the renormalization group flow in this model.Comment: 41 pages, 11 figure

Quantum Fusion of Domain Walls with Fluxes

We study how fluxes on the domain wall world volume modify quantum fusion of two distant parallel domain walls into a composite wall. The elementary wall fluxes can be separated into parallel and antiparallel components. The parallel component affects neither the binding energy nor the process of quantum merger. The antiparallel fluxes, instead, increase the binding energy and, against naive expectations, suppress quantum fusion. In the small flux limit we explicitly find the bounce solution and the fusion rate as a function of the flux. We argue that at large (antiparallel) fluxes there exists a critical value of the flux (versus the difference in the wall tensions), which switches off quantum fusion altogether. This phenomenon of flux-related wall stabilization is rather peculiar: it is unrelated to any conserved quantity. Our consideration of the flux-related all stabilization is based on substantiated arguments that fall short of complete proof.Comment: 17 pages, 3 figure

Relaxing a constraint on the number of messengers in a low-scale gauge mediation

We propose a mechanism for relaxing a constraint on the number of messengers in low-scale gauge mediation models. The Landau pole problem for the standard-model gauge coupling constants in the low-scale gauge mediation can be circumvented by using our mechanism. An essential ingredient is a large positive anomalous dimension of messenger fields given by a large Yukawa coupling in a conformal field theory at high energies. The positive anomalous dimension reduces the contribution of the messengers to the beta function of the standard-model gauge couplings.Comment: 22pages; v2:explanations expanded in sec.3.2, reference adde

Confinement and Localization on Domain Walls

We continue the studies of localization of the U(1) gauge fields on domain walls. Depending on dynamics of the bulk theory the gauge field localized on the domain wall can be either in the Coulomb phase or squeezed into flux tubes implying (Abelian) confinement of probe charges on the wall along the wall surface. First, we consider a simple toy model with one flavor in the bulk at weak coupling (a minimal model) realizing the latter scenario. We then suggest a model presenting an extension of the Seiberg--Witten theory which is at strong coupling, but all theoretical constructions are under full control if we base our analysis on a dual effective action. Finally, we compare our findings with the wall in a "nonminimal" theory with two distinct quark flavors that had been studied previously. In this case the U(1) gauge field trapped on the wall is exactly massless because it is the Goldstone boson of a U(1) symmetry in the bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb phase. We explain why the mechanism of confinement discussed in the first part of the paper does not work in this case, and strings are not formed on the walls.Comment: 55 pp; v2: several remarks adde

QSSR estimate of the BBB_B parameter at next-to-leading order

We compute the leading $\alpha_s$ corrections to the two-point correlator of the $O_{\Delta B=2}$ operator which controls the $B^0 \bar B^0$ mixing. Using this result within the QCD spectral sum rules approach and some phenomenologically reasonable assumptions in the parametrization of the spectral function, we conclude that the vacuum saturation values $B_B\simeq B_{B^*}\simeq 1$ are satisfied within 15\%.Comment: 8 pages, LaTeX, CERN-TH.7140/94, PM 93/16, and KEK Preprint 93-184, two figures appended as a PS fil

Central Charge Anomalies in 2D Sigma Models with Twisted Mass

We discuss the central charge in supersymmetric ${\cal N}=2$ sigma models in two dimensions. The target space is a symmetric K\"ahler manifold, CP$(N-1)$ is an example. The U(1) isometries allow one to introduce twisted masses in the model. At the classical level the central charge contains Noether charges of the U(1) isometries and a topological charge which is an integral of a total derivative of the Killing potentials. At the quantum level the topological part of the central charge acquires anomalous terms. A bifermion term was found previously, using supersymmetry which relates it to the superconformal anomaly. We present a direct calculation of this term using a number of regularizations. We derive, for the first time, the bosonic part in the central charge anomaly. We construct the supermultiplet of all anomalies and present its superfield description. We also discuss a related issue of BPS solitons in the CP(1) model and present an explicit form for the curve of marginal stability.Comment: 30 pages, 1 figure, references adde