Two-loop Yang-Mills diagrams from superstring amplitudes

TL;DR

This paper demonstrates how superstring amplitudes with D-branes and background fields precisely reproduce two-loop Yang-Mills Feynman diagrams, revealing a detailed string-field theory correspondence.

Contribution

It introduces a method to compute twisted period matrix determinants and establishes a one-to-one link between string degenerations and gauge theory diagrams at two loops.

Findings

Superstring amplitudes reproduce two-loop Yang-Mills diagrams.

Twisted (Prym) super differentials encode background field information.

A new computational method for twisted period matrices.

Abstract

Starting from the superstring amplitude describing interactions among D-branes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory Feynman diagrams. A key ingredient in the string construction is represented by the twisted (Prym) super differentials, as their periods encode the information about the background field. We provide an efficient method to calculate perturbatively the determinant of the twisted period matrix in terms of sets of super-moduli appropriate to the degeneration limits. Using this result we show that there is a precise one-to-one correspondence between the degeneration of different factors in the superstring amplitudes and one-particle irreducible Feynman diagrams capturing the gauge theory effective action at the two-loop level.