Gravitational Lensing by Cosmic String Loops
  We calculate the deflection of a light ray caused by the gravitational field of a cosmic string loop in the weak field limit and reduce the problem to a single quadrature over a time slice of the loop's world sheet. We then apply this formalism to the problem of gravitational lensing by cosmic string loops. In particular, we find an analytic solution for the special case of a circular loop perpendicular to the optical axis. As examples of more complicated loops, we consider two loops with higher frequency Fourier modes. The numerical analysis illustrates the general features of loop lenses. Our estimates, using typical parameters for GUT scale loops, show that the stringy nature of loop lenses can be observed for lensing systems involving high redshift galaxies ($z \sim 2$), and we suggest that gravitational lensing can confirm the existence of GUT scale strings if they are the seeds for large scale structure formation. 
Andrew A de Laix and Tanmay Vachaspati