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Multiple cosmic strings in Chern-Simons-Higgs theory with gravity

Lei Cao, Shouxin Chen

Abstract

In this paper, we consider the self-dual equation arising from Abelian Chern-Simons-Higgs theory coupled to the Einstein equations over the plane $\mathbb{R}^2$ and a compact surface $S$. We prove the existence of symmetric topological solutions and non-topological solutions on the plane by using the fixed-point theorem and a shooting method, respectively. A necessary and sufficient condition related to the string number $N$, the Euler characteristic $χ(S)$ of $S$, and the gravitational coupling factor $G$ is given to show the existence of $N$-string solutions over a compact surface.

Multiple cosmic strings in Chern-Simons-Higgs theory with gravity

Abstract

In this paper, we consider the self-dual equation arising from Abelian Chern-Simons-Higgs theory coupled to the Einstein equations over the plane and a compact surface . We prove the existence of symmetric topological solutions and non-topological solutions on the plane by using the fixed-point theorem and a shooting method, respectively. A necessary and sufficient condition related to the string number , the Euler characteristic of , and the gravitational coupling factor is given to show the existence of -string solutions over a compact surface.
Paper Structure (5 sections, 10 theorems, 111 equations)

This paper contains 5 sections, 10 theorems, 111 equations.

Table of Contents

  1. Introduction
  2. Construction of symmetric solutions
  3. Symmetric topological solutions
  4. Symmetric non--topological solutions
  5. Existence of strings over compact surface

Key Result

Theorem 1.1

Under the condition $4\pi G N=1$ and $N\geq1$, if all the points $p_s$ are identical, that is to say, $p_s=p_0, s=1,2,\cdots, N$. Then the equation 1.21 has a symmetric topological solution that vanishes at infinity with the choice and possess the sharp decay behavior

Theorems & Definitions (17)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • ...and 7 more