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 N=(0,2) Two-Dimensional CP(N-1) Model

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the CP(N-1) model with an extra right-handed fermion field and N=(0,2) supersymmetry. This model emerges as a low-energy theory on the worldsheet of the BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by a superpotential of a special type breaking N=2 supersymmetry down to N=1. Using large-N expansion we solve this model to the leading order in 1/N. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete Z_{2N} symmetry is shown to be spontaneously broken down to Z_2; therefore, the worldsheet model has N strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic CP(N-1) model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the N=(2,2) CP(N-1) model which has N degenerate vacua with unbroken supersymmetry, and, on the other hand, with nonsupersymmetric CP(N-1) model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic CP(N-1) model in the large-N limit.Comment: 23 pages, 6 figures/v.2: 2 expressions corrected, minor textual changes, 1 reference adde

Dynamical GUT breaking and mu-term driven supersymmetry breaking

Models for dynamical breaking of supersymmetric grand unified theories are presented. The doublet-triplet splitting problem is absent since the Higgs doublet superfields can be identified with the massless mesons of the strong gauge group whereas there are no massless states corresponding to the colored Higgs fields. Various strong gauge groups SU(Nc), Sp(Nc) and SO(Nc) are examined. In a model with SO(9) strong gauge group, adding the mu-term for the Higgs fields triggers to break supersymmetry in a meta-stable vacuum. The pattern of the supersymmetry breaking parameters is predicted to be the gauge-mediation type with modifications in the Higgs sector.Comment: 23 pages, 1 figure; version to appear in PR

Spontaneous Z2 Symmetry Breaking in the Orbifold Daughter of N=1 Super Yang-Mills Theory, Fractional Domain Walls and Vacuum Structure

We discuss the fate of the Z2 symmetry and the vacuum structure in an SU(N)xSU(N) gauge theory with one bifundamental Dirac fermion. This theory can be obtained from SU(2N) supersymmetric Yang--Mills (SYM) theory by virtue of Z2 orbifolding. We analyze dynamics of domain walls and argue that the Z2 symmetry is spontaneously broken. Since unbroken Z2 is a necessary condition for nonperturbative planar equivalence we conclude that the orbifold daughter is nonperturbatively nonequivalent to its supersymmetric parent. En route, our investigation reveals the existence of fractional domain walls, similar to fractional D-branes of string theory on orbifolds. We conjecture on the fate of these domain walls in the true solution of the Z2-broken orbifold theory. We also comment on relation with nonsupersymmetric string theories and closed-string tachyon condensation.Comment: 37 pages, 7 figures. v2: various significant changes; revisions explained in the introduction. Final version to appear in Phys.Rev.

N=(0,2) Deformation of the N=(2,2) Wess-Zumino Model in Two Dimensions

We construct a simple N=(0,2) deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a "twisted" superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the latter case an extra right-handed fermion field \zeta_R involved in the N=(0,2) deformation plays the role of Goldstino.Comment: 6 pages; v2: 3 references added; final version accepted for publication in PR

On the Significance of the Quantity "A Squared"

We consider the gauge potential A and argue that the minimum value of the volume integral of A squared (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice simulation comparing compact and non-compact ``photodynamics'' shows a jump in this quantity at the phase transition, supporting this idea.Comment: 6 pages, one figur

A remark on collisions of domain walls in a supersymmetric model

The process of collision of two parallel domain walls in a supersymmetric model is studied both in effective Lagrangian approximation and by numerical solving of the exact classical field problem. For small initial velocities we find that the walls interaction looks like elastic reflection with some delay. It is also shown that in such approximation internal parameter of the wall may be considered as a time-dependent dynamical variable.Comment: 6 pages, LaTeX, 3 figures (eps), fig. 2 correcte

Domain Lines as Fractional Strings

We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $\beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $\beta=0$ the BPS-saturated domain wall interpolating between them has a moduli space parameterized by a U(1) phase $\sigma$ which can be promoted to a scalar field in the effective low-energy theory on the wall world-volume. At small nonvanishing $\beta$ this field gets a sine-Gordon potential. As a result, only two discrete degenerate BPS domain walls survive. We find an explicit solitonic solution for domain lines -- string-like objects living on the surface of the domain wall which separate wall I from wall II. The domain line is seen as a BPS kink in the world-volume effective theory. We expect that the wall with the domain line on it saturates both the $\{1,0\}$ and the $\{{1/2},{1/2}\}$b central charges of the bulk theory. The domain line carries the magnetic flux which is exactly 1/2 of the flux carried by the flux tube living in the bulk on each side of the wall. Thus, the domain lines on the wall confine charges living on the wall, resembling Polyakov's three-dimensional confinement.Comment: 28 pages, 13 figure, v2 typos fixed and reference adde

S-Track Stabilization of Heterotic de Sitter Vacua

We present a new mechanism, the S-Track, to stabilize the volume modulus S in heterotic M-theory flux compactifications along with the orbifold-size T besides complex structure and vector bundle moduli stabilization. The key dynamical ingredient which makes the volume modulus stabilization possible, is M5-instantons arising from M5-branes wrapping the whole Calabi-Yau slice. These are natural in heterotic M-theory where the warping shrinks the Calabi-Yau volume along S^1/Z_2. Combined with H-flux, open M2-instantons and hidden sector gaugino condensation it leads to a superpotential W which stabilizes S similar like a racetrack but without the need for multi gaugino condensation. Moreover, W contains two competing non-perturbative effects which stabilize T. We analyze the potential and superpotentials to show that it leads to heterotic de Sitter vacua with broken supersymmetry through non-vanishing F-terms.Comment: 16 pages, 2 figures; final PRD versio

Quantum Mechanics of the Vacuum State in Two-Dimensional QCD with Adjoint Fermions

A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) has been performed. The main emphasis is put on the symmetry properties related to the homotopically non-trivial gauge transformations and the discrete axial symmetry of this model. Within a gauge fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss's law on the other hand is exhibited. As a result, a consistent description of the residual $Z_N$ gauge symmetry (for SU(N)) and the ``axial anomaly" emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.Comment: 44 pages; for hardcopies of figures, contact [email protected]