Self-dual cosmic strings and gravitating vortices in gauged sigma models

Abstract

Cosmic strings are considered in two types of gauged sigma models, which generalize the gravitating Abelian Higgs model. The two models differ by whether the U(1) kinetic term is of the Maxwell or Chern-Simons form. We obtain the self-duality conditions for a general two-dimensional target space defined in terms of field dependent "dielectric functions". In particular, we analyze analytically and numerically the equations for the case of O(3) models (two-sphere as target space), and find cosmic string solutions of several kinds as well as gravitating vortices. We classify the solutions by their flux and topological charge. We note an interesting connection between the Maxwell and Chern-Simons type models, which is responsible for simple relations between the self-dual solutions of both types. There is however a significant difference between the two systems, in that only the Chern-Simons type sigma model gives rise to spinning cosmic vortices.

Nonsingular stationary global strings

“…for fields that satisfy |Φ| → ∞ as r → ∞. It is interesting to note that the linear sigma model (E(|φ|) = 1) needs for self-duality a potential which is unbounded from below, which is a property shared by other systems [26].…”

“…ref. [26] and references therein). So we will start in the simplest case of self-dual solutions in the D = 3 system.…”

Two species of semi-local cosmic strings in Abelian gauged $\mathbb{CP}^2$-sigma models coupled to gravity

“…In that situation the target manifold of the scalar fields reduces to CP 1 , or S 2 , and we have thus cosmic strings with values on the sphere. Vortices and cosmic strings on the sphere were previously studied by means of the Bogomolny equations in [23,24,25] and we will here revisit this problem to provide some new results for the non self-dual case, where the main novelty is the presence of a non-vanishing function A(x). Thus, we show in figures 7 and 8 the profile of this function, and also of the other metric coefficient h(x), where we have considered the effect of several values of the gravitational coupling for scalar potentials of type I and II, namely with β = 0.8 and β = 1.5.…”

“…Also, the non-commutative version of the AHM has been studied, both in its original formulation [21] or with a dielectric function in place [22]. These modifications made it possible to ponder variants of the AHM in which the Higgs field is valued on a compact manifold like a sphere [23,24], and situations of this type have been also studied in the cosmic string context [25]. Another direction in which the Abelian Higgs model has been extended is the addition of more scalar fields, giving rise to the so called semi-local models.…”

Dirac Quantization of a Nonminimal Gauged O(3) Sigma Model

“…In particular soliton solutions of the gauged O(3) Chern-Simons model may be relevant in planar condensed matter systems 1,2,3 . Recently gauged gravitating nonlinear sigma model was considered in order to obtain self-dual cosmic string solutions 4 . The canonical quantization of nonlinear gauged sigma models has been studied by some authors in the context of the CP 1 sigma model.…”