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Reconnection of Non-Abelian Cosmic Strings

Koji Hashimoto, David Tong

Abstract

Cosmic strings in non-abelian gauge theories naturally gain a spectrum of massless, or light, excitations arising from their embedding in color and flavor space. This opens up the possibility that colliding strings miss each other in the internal space, reducing the probability of reconnection. We study the topology of the non-abelian vortex moduli space to determine the outcome of string collision. Surprisingly we find that the probability of classical reconnection in this system remains unity, with strings passing through each other only for finely tuned initial conditions. We proceed to show how this conclusion can be changed by symmetry breaking effects, or by quantum effects associated to fermionic zero modes, and present examples where the probability of reconnection in a U(N) gauge theory ranges from 1/N for low-energy collisions to one at higher energies.

Reconnection of Non-Abelian Cosmic Strings

Abstract

Cosmic strings in non-abelian gauge theories naturally gain a spectrum of massless, or light, excitations arising from their embedding in color and flavor space. This opens up the possibility that colliding strings miss each other in the internal space, reducing the probability of reconnection. We study the topology of the non-abelian vortex moduli space to determine the outcome of string collision. Surprisingly we find that the probability of classical reconnection in this system remains unity, with strings passing through each other only for finely tuned initial conditions. We proceed to show how this conclusion can be changed by symmetry breaking effects, or by quantum effects associated to fermionic zero modes, and present examples where the probability of reconnection in a U(N) gauge theory ranges from 1/N for low-energy collisions to one at higher energies.

Paper Structure

This paper contains 12 sections, 40 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Non-Abelian Cosmic Strings
  3. The Classical Reconnection of Cosmic Strings
  4. Reconnection of $U(1)$ Strings
  5. The Moduli Space of Non-Abelian Vortices
  6. Reconnection of $U(2)$ Strings
  7. Reconnection of $U(N)$ Strings
  8. Symmetry Breaking and Quantum Effects
  9. Symmetry Breaking and Monopole Pair Creation
  10. Quantum Effects
  11. Fermionic Zero Modes
  12. Summary and Conclusions

Figures (3)

  • Figure 1: The reconnection cosmic strings. Slicing vertically, one sees a vortex-anti-vortex pair annihilate. Slicing horizontally, one sees two vortices scattering at right angles.
  • Figure 2: Right Angle Scattering: The view from the moduli space (on the left) and in real space (on the right).
  • Figure 3: Reconnected strings of different kinds. The blobs are a monopole and an anti-monopole. The dashed lines are original configuration of the intersecting strings.