Superstring amplitudes from BCJ numerators at one loop

Abstract

We find a direct map that determines moduli-space integrands for one-loop superstring amplitudes in terms of field-theory loop integrands in the BCJ form. The latter can be computed using efficient unitarity methods, so our map provides an alternative to worldsheet CFT techniques. This construction is a one-loop higher-point analogue of a recent conjecture for the three-loop four-point superstring amplitude. Based on the one-loop chiral-splitting representation, we show how all coefficients of an ansatz for the superstring can be identified with field-theory BCJ numerators, up to at least 7-point amplitudes. Moreover, we obtain partial results for all higher-point amplitudes. The monodromy constraints associated to chiral splitting play a crucial role in determining coefficients of the ansatz that, naively, are not fixed by the field-theory limit. Taking a field-theory perspective, our ansatz for the superstring implies by construction the existence of one-loop BCJ numerators at any multiplicity.