Six-Derivative Yang-Mills Couplings in Heterotic String Theory

TL;DR

This paper analyzes six-derivative couplings in heterotic string theory, determining invariant bases, applying T-duality constraints, and reducing couplings to a canonical form with 85 independent parameters.

Contribution

It provides a comprehensive classification and reduction of six-derivative bosonic couplings in heterotic string theory using gauge invariance and T-duality constraints.

Findings

Identified 801 independent couplings before constraints.

Derived 468 relations from T-duality constraints.

Reduced to 85 independent couplings after field redefinitions.

Abstract

In this work, we present a comprehensive analysis of the structure of six-derivative bosonic couplings in heterotic string theory. First, we determine the maximal covariant and Yang-Mills gauge invariant basis, which consists of 801 independent coupling constants. By imposing T-duality constraints on the circular reduction of these terms, we obtain 468 relations between the coupling constants at the six-derivative order and the known couplings at lower derivative orders. Through the use of field redefinitions, we are able to eliminate the remaining 333 coupling constants. Remarkably, we find that the Yang-Mills field strength only appears through the trace of two field strengths or their derivatives. Finally, we perform further field redefinition to rewrite the remaining couplings in a canonical form characterized by 85 independent couplings.