Title: Odd-Derivative Couplings in Heterotic Theory

Abstract: In this paper, our focus is on exploring the gauge invariant basis for bosonic couplings within the framework of heterotic string theories, specifically examining 3-, 5-, and 7-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 5 Yang-Mills field strength are non-zero.