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Abstract
En 中文
We reformulate tree-level amplitudes in open superstring theory (type-I) in terms of stringy Tr(43) amplitudes with various kinematical shifts in the curve-integral formulation: while the bosonic-string amplitude with n pairs of scaffolding scalars comes from a particularly simple shift of the Tr(43) one (corresponding to n length-2 cycles), the analogous superstring amplitude requires correction terms given by bosonic-string amplitudes with longer, even-length cycles, which are also Tr(43) ones at shifted kinematics dictated by the cycles; in total it is expressed as a sum of (2n-3)!! shifted amplitudes originated from the expansion of a reduced Pfaffian. Upon taking n scaffolding residues, this leads to a new formula of the n-gluon superstring amplitude, which is manifestly symmetric in n-1 legs, as a gauge-invariant combination of mixed bosonic string amplitudes with gluons and scalars, which come from length-2 cycles and longer ones respectively (the total sum is associated with the expansion a n x n symmetrical determinant); the corresponding prefactors are nested commutators of 2n-gon kinematical variables, which nicely become traces of field-strengths for those legs corresponding to scalars in the mixed amplitudes. These interesting linear combinations of bosonic string amplitudes must guarantee the cancellation of tachyon poles and F3 vertices etc., and they give new relations between the superstring amplitude and its bosonic-string building blocks to all orders in the alpha ' expansion (the first order gives a new formula for gluon amplitudes with a single F3 insertion in terms of Yang-Mills-scalar amplitudes). We provide both the worldsheet and curve-integral derivations, and discuss applications to heterotic and type II cases.
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