We discuss the formation of cosmic strings or macroscopic color flux tubes at the phase transition from the deconfinement to confinement phase in pure Yang–Mills (YM) theory, such as $\mathrm{SU}(N)$, $\mathrm{Sp}(N)$, $\mathrm{SO}(N)$, and $\text{Spin}(N)$, based on the current understanding of theoretical physics. According to the holographic dual descriptions, the cosmic strings are dual to fundamental strings or wrapped D-branes in the gravity side depending on the structure of the gauge group, and the reconnection probability is suppressed by $\mathcal{O}(N^{-2})$ and $e^{-\mathcal{O}(N)}$, respectively. The pure YM theory thus provides a simple realization of cosmic F- and D-strings without the need for a brane-inflationary scenario or extra dimension. We also review the stability of cosmic strings based on the concept of 1-form symmetry, which further implies the existence of a baryon vertex in some YM theory. We calculate the gravitational wave spectrum that is emitted from the cosmic strings based on an extended velocity-dependent one-scale model and discuss its detectability based on ongoing and planned gravitational-wave experiments. In particular, the SKA and LISA can observe gravitational signals if the confinement scale is higher than $\mathcal{O}({10}^{12})\mathrm{GeV}$ and $\mathcal{O}({10}^{10})\mathrm{GeV}$ for $\mathrm{SU}(N)$ with $N=\mathcal{O}(1)$, respectively.

• Received 9 May 2022
• Accepted 17 November 2022

DOI:https://doi.org/10.1103/PhysRevD.106.123515

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Published by the American Physical Society