What is the concept of cosmic strings? What is the concept of cosmic strings? Is it related to the strings in the string theory, and if it is, then how?
 A: In a paper by R. Gregory, Effective Action and Motion of a Cosmic String, the concept is explained well:


In high energy physics, a defect will generically occur during a symmetry breaking process where different parts of a medium choose different vacuum energy configurations, and the non-compatibility of these different vacua forces a sheet, line or point of energy where these non-compatible vacua meet... A defect may be topological, in that it is the topology of the vacuum that simultaneously allows formation, and prevents dissipation...


The fourth order effective action of the string is given by,
$$S=-\mu\int d^2\sigma \sqrt{-\gamma} \left[ 1-r_s^2 \frac{\alpha_1}{\mu}\mathcal{R}+r^4_s \left( \frac{\alpha_2}{\mu}\mathcal{R}^2 + \frac{\alpha_3}{\mu}K_{i\mu\nu}\mathcal{K}^{\mu\nu}_j  \mathcal{K}_{i\lambda \rho} \mathcal{K}^{\lambda\rho}_j \right)\right]$$
where $\alpha_i$ are numerical coefficients, $\mu$ the tension of the string, and all geometric quantities evaluated with respect to the worldsheet of the string, which is the manifold traced out by the motion of the string. The worldsheet itself is within the target space or 'spacetime.' The $\mathcal{K}$ terms are the extrinsic curvature of the worldsheet. As R. Gregory states, a priori, it is difficult to determine whether these affect the rigidity of the string.
