Six-Derivative Yang-Mills Couplings in Heterotic String Theory

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.

arXiv comment24 pages, Latex file, no figure; v2: the version appears in SciPost Physics

References in corpus (16)

• Noncompact Symmetries in String Theory
• xTras: a field-theory inspired xAct package for Mathematica
• Twisting Classical Solutions in Heterotic String Theory
• T-duality and ${\alpha }^{\prime }$-corrections
• Duality Invariant Cosmology to all Orders in ${\alpha }^{\prime }$
• Solution--Generating Transformations and the String Effective Action
• Heterotic Effective Action and Duality Symmetries Revisited
• The Odd story of ${\alpha }^{\prime }$-corrections
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• alpha'-Corrections to Heterotic Superstring Effective Action Revisited
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• T-duality Constraints on Higher Derivatives Revisited
• Four-derivative couplings via T-duality constraint
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• $R^4$ terms in supergravities via T-duality constraint
• Minimal independent couplings at order ${\alpha }^{\prime 2}$