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Superstring amplitudes as a Mellin transform of supergravity. (English) Zbl 1282.81153

Summary: At the tree level, the maximally helicity violating amplitudes of \(N\) gauge bosons in open superstring theory and of \(N\) gravitons in supergravity are known to have simple representations in terms of tree graphs. For superstrings, the graphs encode integral representations of certain generalized Gaussian hypergeometric functions of kinematic invariants while for supergravity, they represent specific kinematic expressions constructed from spinor-helicity variables. We establish a superstring/supergravity correspondence for this class of amplitudes, by constructing a mapping between the positions of gauge boson vertices at the disk boundary and the helicity spinors associated to gravitons. After replacing vertex positions by a larger set of \(\frac{N(N-3)}{2}\) coordinates, the superstring amplitudes become (multiple) Mellin transforms of supergravity amplitudes, from the projective space into the dual Mellin space of \(\frac{N(N-3)}{2}\) kinematic invariants. Similarly, inverse Mellin transforms transmute open superstrings into supergravity. We elaborate on the properties of multiple Mellin and inverse Mellin transforms in the framework of superstring/supergravity correspondence.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E50 Supergravity
83C45 Quantization of the gravitational field
05C05 Trees
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