Reconnection of Colliding Cosmic Strings

For vortex strings in the Abelian Higgs model and D-strings in superstring theory, both of which can be regarded as cosmic strings, we give analytical study of reconnection (recombination, inter-commutation) when they collide, by using effective field theories on the strings. First, for the vortex strings, via a string sigma model, we verify analytically that the reconnection is classically inevitable for small collision velocity and small relative angle. Evolution of the shape of the reconnected strings provides an upper bound on the collision velocity in order for the reconnection to occur. These analytical results are in agreement with previous numerical results. On the other hand, reconnection of the D-strings is not classical but probabilistic. We show that a quantum calculation of the reconnection probability using a D-string action reproduces the nonperturbative nature of the worldsheet results by Jackson, Jones and Polchinski. The difference on the reconnection -- classically inevitable for the vortex strings while quantum mechanical for the D-strings -- is suggested to originate from the difference between the effective field theories on the strings.Comment: 29 pages, 14 eps figures, JHEP style; references added, typos correcte

Heterotic Vortex Strings

We determine the low-energy N=(0,2) worldsheet dynamics of vortex strings in a large class of non-Abelian N=1 supersymmetric gauge theories.Comment: 44 pages, 3 figures. v2: typos corrected, reference adde

Cosmic Superstring Scattering in Backgrounds

We generalize the calculation of cosmic superstring reconnection probability to non-trivial backgrounds. This is done by modeling cosmic strings as wound tachyon modes in the 0B theory, and the spacetime effective action is then used to couple this to background fields. Simple examples are given including trivial and warped compactifications. Generalization to $(p,q)$ strings is discussed.Comment: 12 pages, 2 figures; v2: references adde

Counting Chiral Operators in Quiver Gauge Theories

We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number of D-branes. Explicit formulae are given for few examples, including C^3/Z_3, F_0, and dP_1.Comment: 75 pages, 22 figure

Solitons in Supersymmety Breaking Meta-Stable Vacua

In recently found supersymmetry-breaking meta-stable vacua of the supersymmetric QCD, we examine possible exsitence of solitons. Homotopy groups of the moduli space of the meta-stable vacua show that there is no nontrivial soliton for SU(N_c) gauge group. When U(1)_B symmetry present in the theory is gauged, we find non-BPS solitonic (vortex) strings whose existence and properties are predicted from brane configurations. We obtain explicit classical solutions which reproduce the predicitions. For SO(N_c) gauge group, we find there are solitonic strings for N = N_f-N_c+4 = 2, and Z_2 strings for the other N. The strings are meta-stable as they live in the meta-stable vacua.Comment: 30 pages, 14 figures, Comments on stability of non-BPS vortices are added, Comments on sigma model solitons are added, An appendix is adde

Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories

Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint mass terms. For generic internal orientations the classical force between two vortices can be attractive or repulsive. On the other hand, the mass of the scalars in the theory is always less than that of the vector bosons; also, the force between two vortices with the same CP^1 orientation is always attractive: for these reasons we interpret our model as a non-Abelian generalization of type I superconductors. We compute the effective potential in the limit of two well separated vortices. It is a function of the distance and of the relative colour-flavour orientation of the two vortices; in this limit we find an effective description in terms of two interacting CP^1 sigma models. In the limit of two coincident vortices we find two different solutions with the same topological winding and, for generic values of the parameters, different tensions. One of the two solutions is described by a CP^1 effective sigma model, while the other is just an Abelian vortex without internal degrees of freedom. For generic values of the parameters, one of the two solutions is metastable, while there are evidences that the other one is truly stable.Comment: 35 pages, 8 figures. v2: fixed typos and added small comments, v3 removed an unecessary figur

Non-abelian vortices on compact Riemann surfaces

We consider the vortex equations for a U(n) gauge field coupled to a Higgs field with values on the n times n square matrices. It is known that when these equations are defined on a compact Riemann surface, their moduli space of solutions is closely related to a moduli space of tau-stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the Higgs matrix, we show that the vortex solutions are entirely characterized by (1) the location in the surface of the zeros of the determinant of the Higgs matrix and (2) by the choice of a vortex internal structure at each of these zeros. We describe explicitly the vortex internal spaces and show that they are compact and connected spaces.Comment: 17 pages; v2: typos corrected, as will appear in CM

The Shape of Branes Pulled by Strings

We examine the system where a string stretches between pair of D-branes, and study the bending of the D-brane caused by the tension of the string. If the distance between the pair of D-branes is sent to infinity, the tension of the string stretching between them is strong enough to pull the spike all the way to infinity. We study the shape of these spikes when the branes are finite distance apart using two different methods. First, we consider a string stretched between a pair of D2-branes in type IIA theory by going to the M-theory limit in which all of these branes are M-theory 2-branes embedded along a holomorphic curve. Second, we consider a D-string stretched between a pair of D3-branes in type IIB theory and infer the geometry of the D3-brane embeddings from the configuration of the adjoint scalar field in the magnetic monopole solution of Prasad and Sommerfield. The case of fundamental string stretching between a pair of D3-branes follows from S-duality. The energy of these configurations matches the expected value based on fundamental string and D-string tensions.Comment: 22 pages, 5 figures, uses psfig.sty; typos corrected; references adde

Static Interactions of non-Abelian Vortices

Interactions between non-BPS non-Abelian vortices are studied in non-Abelian U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The distinctive feature of a non-Abelian vortex is the presence of an internal CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of the couplings, the vortices are BPS and there is no net force between two static parallel vortices at arbitrary distance. On the other hand, for generic values of the couplings the interactions between two vortices depend non-trivially on their relative internal orientations. We discuss the problem both with a numerical approach (valid for small deviations from the BPS limit) and in a semi-analytical way (valid at large vortex separations). The interactions can be classified with respect to their asymptotic property at large vortex separation. In a simpler fine-tuned model, we find two regimes which are quite similar to the usual type I/II Abelian superconductors. In the generic model we find other two new regimes: type I*/II*. Unlike the type I (type II) case, where the interaction is always attractive (repulsive), the type I* and II* have both attractive and repulsive interactions depending on the relative orientation. We have found a rich variety of interactions at small vortex separations. For some values of the couplings, a bound state of two static vortices at a non-zero distance exists.Comment: 36 pages, 13 figures; v2 a small comment and a reference adde

QCD String as Vortex String in Seiberg-Dual Theory

We construct a classical vortex string solution in a Seiberg-dual theory of N=1 supersymmetric SO(N_c) QCD which flows to a confining phase. We claim that this vortex string is a QCD string, as previouly argued by M.Strassler. In SO(N_c) QCD, it is known that stable QCD strings exist even in the presence of dynamical quarks. We show that our vortex strings are stable in the Seiberg-dual theory.Comment: 15 pages, 1 figur