One-Loop Double Copy Relation in String Theory

We discuss relations between closed and open string amplitudes at one loop. While at tree level these relations are known as Kawai-Lewellen-Tye (KLT) and/or double copy relations, here we investigate how such relations are manifested at one loop. Although, we find examples of one-loop closed string amplitudes that can strikingly be written as sum over squares of one-loop open string amplitudes, generically the one-loop closed string amplitudes assume a form reminiscent of the one-loop double copy structure of gravitational amplitudes involving a loop momentum. This double copy structure represents the one-loop generalization of the KLT relations.