On the field theory expansion of superstring five point amplitudes

TL;DR

This paper presents a recursive algorithm for expanding superstring five point amplitudes, simplifying calculations and enabling proofs of maximal transcendentality and conjectures, with applications to closed string amplitudes and symmetry classifications.

Contribution

Introduces a recursive expansion method for superstring five point amplitudes that simplifies analysis and proves maximal transcendentality, also applying Molien's theorem for symmetry classification.

Findings

The expansion reduces to simple symbolic manipulations.

The method verifies conjectures to high order.

Constructs a basis for symmetric polynomials of external legs.

Abstract

A simple recursive expansion algorithm for the integrals of tree level superstring five point amplitudes in a flat background is given which reduces the expansion to simple symbol(ic) manipulations. This approach can be used for instance to prove the expansion is maximally transcendental to all orders and to verify several conjectures made in recent literature to high order. Closed string amplitudes follow from these open string results by the KLT relations. To obtain insight into these results in particular the maximal R-symmetry violating amplitudes (MRV) in type IIB superstring theory are studied. The obtained expansion of the open string amplitudes reduces the analysis for MRV amplitudes to the classification of completely symmetric polynomials of the external legs, up to momentum conservation. Using Molien's theorem as a counting tool this problem is solved by constructing an explicit nine element basis for this class. This theorem may be of wider interest: as is illustrated at higher points it can be used to calculate dimensions of polynomials of external momenta invariant under any finite group for in principle any number of legs, up to momentum conservation.