Abstract
We present a new method, exact in α^{'}, to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the moduli-space integrand of all amplitudes with one massive state using Berends-Giele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional type-I and type-II superstrings.
Highlights
Introduction.—The historical origin and the discovery of key features of string theory can be attributed to the study of its scattering amplitudes
Computations and structural properties of string amplitudes rely on exactly solvable correlation functions of vertex operators in a two-dimensional conformal field theory (CFT)
Tree-level amplitudes of n massless states of the open superstring [8,9] and the open bosonic string [10,11] can be factorized into scalar integrals over moduli spaces of punctured disk worldsheets and quantum field theory (QFT) building blocks carrying all the dependence on the external polarizations
Summary
VL⊗R 1⁄4 V L ⊗ VReik·X; ð1Þ where the polarization data factorizes into holomorphic and antiholomorphic pieces, respectively, VR and V L. The massive states can be viewed as a double copy of a tachyon, V T 1⁄4 1, with the first mass level of the open superstring [30] This construction hinges on the twisted level-matching condition. The conventional and twisted string amplitudes, respectively, Mþ and M−, only differ in the Koba-Nielsen factor (3) and can be cast as MÆð1;. Both explicitly factorize the main quantities of interest here: the chiral correlators IR (I L). Field-theory perspective.—We here translate the threepoint amplitudes M− of one massive vertex (5) and two gauge multiplets into the corresponding QFT Feynman vertices. Lagrangian of 10D N 1⁄4 1 SYM, and the combined Feynman rules suffice to determine the chiral correlators IR for one massive state and any number of massless ones
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