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.

• Received 14 October 2023
• Revised 27 February 2024
• Accepted 8 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.191602

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Published by the American Physical Society