Four-graviton one-loop closed superstring amplitudes in the celestial basis factor out the α' dependence, and the field theory limit commutes with the Mellin transform for all values of the cross-ratio.
Superstring/Supergravity Mellin Correspondence in Grassmannian Formulation
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abstract
We extend the recently established Mellin 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 and Mellin transformed into generalized hypergeometric functions of Mandelstam invariants.
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Celestial closed strings at one-loop
Four-graviton one-loop closed superstring amplitudes in the celestial basis factor out the α' dependence, and the field theory limit commutes with the Mellin transform for all values of the cross-ratio.