Abstract
In our previous work, we found new types of the cosmic string solutions in the Abelian-Higgs model with an enhanced U(1) global symmetry. We dubbed those solutions as the compensated/uncompensated strings. The compensated string is similar to the conventional cosmic string in the Abrikosov-Nielsen-Olesen (ANO) string, around which only the would-be Nambu-Goldstone (NG) boson winds. Around the uncompensated string, on the other hand, the physical NG boson also winds, where the physical NG boson is associated with the spontaneous breaking of the enhanced symmetry. Our previous simulation in the 2+1 dimensional spacetime confirmed that both the compensated/uncompensated strings are formed at the phase transition of the symmetry breaking. Non-trivial winding of the physical NG boson around the strings potentially causes the so-called axion domain- wall problem when the model is applied to the axion model. In this paper, we perform simulation in the 3+1 dimensional spacetime to discuss the fate of the uncompensated strings. We observe that the evolution of the string-network is highly complicated in the 3+1 dimensional simulation compared with that seen in the previous simulation. Despite such complications, we find that the number of the uncompensated strings which could cause can be highly suppressed at late times. Our observation suggests that the present setup can be applied to the axion model without suffering from the axion domain-wall problem.
Highlights
In our previous work [1], we performed classical lattice simulation of the timeevolution in the spacetime of the 2+1 dimension (2+1 D). (The earlier numerical simulation of the vortex formation in a similar setup has been performed in [20], which exhibits consistent features with our simulations in [1].) The simulation confirmed the ubiquitous formation of the uncompensated strings at the phase transition
In our previous work, we found new types of the cosmic string solutions in the Abelian-Higgs model with an enhanced U(1) global symmetry
Our previous simulation in the 2+1 dimensional spacetime confirmed that both the compensated/uncompensated strings are formed at the phase transition of the symmetry breaking
Summary
We summarize the model setup. We review the compensated/uncompensated string solutions, as well as the results of the simulation in the 2+1 D spacetime [1]. The model possesses an U(1)global symmetry in addition to the U(1)local symmetry. Such U(1)global symmetry naturally appears as an accidental symmetry in the renormalizable theory when |q1| + |q2| is larger than 4. There appear two NG modes, where one corresponds to the would-be NG boson (b), and another one is the gauge-invariant NG modes (a). We can extract these two modes from the phase components of the complex scalar fields, φ1. We can see the component a is invariant under the U(1)local gauge transformation, a1/f1 → a1/f1 + q1α , a2/f2 → a2/f2 + q2α ,. The domain of the gauge invariant axion is given by, a Fa
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