Abstract

We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking is not localized. This new structure can lead to corrections to the mass scale of the defects which is not captured by a simple effective theory obtained by integrating out the extra dimension. We also consider the Higgsless model of symmetry breaking and show that no finite energy defects appear in some situations where they might have been expected.

Highlights

  • In the presence of an extra dimension, defect solutions have been extended from the 4 dimensional case if the extra dimension is homogeneous [21]

  • We will show that this symmetry breaking can be understood from the perspective of a simple 4 dimensional effective theory, and that the effective theory does not capture enough of the 5 dimensional physics to correctly predict the tension of the resulting strings

  • We have seen that the vacuum expectation value (VEV) of the field on the symmetry breaking brane is not set by v alone as it would be if the bulk did not exist or if m = 0

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Summary

Global Symmetry Breaking

We wish to begin consideration of localized symmetry breaking with a very simple example where it is possible to visualize the solutions and where some aspects of the problem can be solved analytically. In preparation for comparison with the extra dimensional case, we first review the standard breaking of a global U (1) symmetry in 3 + 1 large dimensions. To make comparison with the 5 dimensional case later, we leave the v4 explicit These winding solutions must reduce to the vacuum far from the core of the string and have continuous field values in the core, so f (r) has the boundary conditions:. If we suppose that there is a network of strings with positive and negative winding number separated by some characteristic scale R we may impose a large distance cutoff on the integral In this case the string tension scales with the log of the cutoff scale: μ4 ∼ 2πv42n2 ln(v4R)

Symmetry Breaking with a Homogeneous Extra Dimension
Symmetry Breaking Localized on a Brane
The Four Dimensional Effective Action
Non-Trivial Winding
Limiting Behavior
The Local String
The Four Dimensional Local String
Local Symmetry with Brane Localized Higgs
Numerical Comparison
Higgsless Models
Higgsless Equations of Motion and Boundary Conditions
Generalized Derrick’s Theorem
Summary
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