Existence of non-topological multi-string solutions for a gravitational 𝑂(3) gauge field model

Choi, Nari; Han, Jongmin

doi:10.1090/proc/14182

Existence of non-topological multi-string solutions for a gravitational $O(3)$ gauge field model
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by Nari Choi and Jongmin Han

Proc. Amer. Math. Soc. 147 (2019), 1429-1445

DOI: https://doi.org/10.1090/proc/14182

Published electronically: December 31, 2018

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Abstract:

In this paper, we consider the self-dual equation arising from the Maxwell gauged $O(3)$ model coupled with gravity. We prove the existence of non-topological multi-string solutions and obtain their decay estimates at infinity. Using the decay rates, we compute the static energy, the magnetic flux, and the total Gaussian curvature corresponding to our solutions. Our solutions are constructed by a perturbation argument with an application of the Implicit Function Theorem.

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