Odd-derivative couplings in heterotic theory

In this paper, our focus is on exploring the gauge-invariant basis for bosonic couplings within the framework of heterotic string theories, specifically examining three-, five-, and seven-derivative terms. We thoroughly analyze the invariance of these couplings under T-duality transformations and make a notable observation: the T-duality constraint enforces the vanishing of these couplings. We speculate that this result likely holds true for all higher odd-derivative couplings as well. This is unlike the result in type I superstring theory, where, for example, the couplings of five Yang-Mills field strengths are nonzero. The vanishing of couplings is consistent with the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>O</a:mi><a:mo stretchy="false">(</a:mo><a:mi>d</a:mi><a:mo>,</a:mo><a:mi>d</a:mi><a:mo>+</a:mo><a:mn>16</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> symmetry of the cosmological reduction of the effective action. Published by the American Physical Society 2024