Discovery-HET Seminar: Stephan Stieberger – University of Copenhagen

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Discovery-HET Seminar: Stephan Stieberger

Speaker: Stephan Stieberger (MPI Munich)

Title: On Superstring/Supergravity Mellin Correspondence in Grassmannian Formulation

Abstract: 

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. 
Furthermore, we extend this correspondence of supergravity and superstring amplitudes to the case of arbitrary helicity configurations. The amplitudes are discussed in the framework of Grassmannian varieties. We generalize Hodges' determinant to a function of two sets of independent coordinates and show that tree-level supergravity amplitudes can be obtained by contour integrations of both sets in separate Grassmannians while in superstring theory, one set of coordinates is identified with string vertex positions at the disk boundary.
After replacing vertex positions by a larger set of 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 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.