Description
Are perturbative superstring amplitudes for massless external states just an $
\alpha'$ dressing of super-Yang-Mills/supergravity? This is the case at tree level, where
the worldsheet correlators at $n$ points can be written in a natural worldsheet basis, such
that the kinematic coefficients are BCJ numerators of super-Yang-Mills/supergravity
amplitudes, with the non-trivial $\alpha'$ dependence carried only by the Koba-Nielsen
factor. Motivated by this construction, we present for the first time a complete worldsheet
basis of one-loop superstring correlators at $n$ points. All the kinematic coefficients
associated to non-cusp basis elements are identified with pieces of one-loop BCJ
numerators of super-Yang-Mills/supergravity. This determines the superstring correlators
up to 15 points in terms of field theory. Starting at 16 points (modular weight 12), the
worldsheet basis may include cusp forms, which vanish in the field-theory degeneration,
such that the associated coefficients cannot be fixed in this manner. Therefore, the oneloop
answer to our initial question is determined, at high multiplicity, by whether the
coefficients of cusp basis elements vanish or not. As a by-product of our construction, we
present new constraints on the field-theory limit that result from string modularity. These
are expressed as additional relations among one-loop BCJ numerators in maximal super-
Yang-Mills/supergravity starting at 6 points.