Carlos Rodriguez (MPI Leipzig):

Double-copy formulas on punctured Riemann surfaces

Abstract: The Kawai-Lewellen-Tye (KLT) relations, discovered in 1986, express tree-level closed-string amplitudes as a bilinear combination of open string amplitudes (also known as "double copy"). These relations come out naturally from the view point of twisted de Rham theory: tree-level string amplitudes are naturally hypergeometric integrals -- or twisted periods -- in that framework. Here, I will sketch the construction of hypergeometric integrals on punctured Riemann surfaces of genus-g, inspired by g-loop string amplitudes. These integrals exhibit the double-copy, and point towards a g-loop generalization of the KLT relations.