Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

TL;DR

This paper investigates how maximal supersymmetry constrains multi-loop contributions to four-gluon scattering in string and field theories, revealing that certain terms are limited to low loop orders, affecting ultraviolet divergence behavior.

Contribution

It provides a detailed analysis of non-renormalization conditions for four-gluon scattering amplitudes in supersymmetric theories, extending understanding of loop contributions and divergences.

Findings

Double-trace terms receive contributions only up to two loops.

Single-trace terms receive contributions at all loop orders.

Supersymmetry constrains ultraviolet divergences in gauge and gravity theories.

Abstract

The constraints imposed by maximal supersymmetry on multi-loop contributions to the scattering of four open superstrings in the U(N) theory are examined by use of the pure spinor formalism. The double-trace term k^2 t_8(tr F^2)^2 (where k represents an external momentum and F the Yang--Mills field strength) only receives contributions from L<=2 (where L is the loop number) while the single-trace term k^2 t_8(tr F^4) receives contributions from all L. We verified these statements up to L=5, but arguments based on supersymmetry suggest they extend to all L. This explains why the single-trace contributions to low energy maximally supersymmetric Yang--Mills field theory are more divergent in the ultraviolet than the double-trace contributions. We also comment further on the constraints on closed string amplitudes and their implications for ultraviolet divergences in N=8 supergravity.