Four-Derivative Yang-Mills Couplings in Heterotic Theory through T-Duality

This study delves into the dimensional reduction of the classical effective action of heterotic string theory on a circle, along with its T-duality symmetry, with the aim of identifying the bosonic couplings. To achieve this, we propose a truncation scheme for the generalized Buscher rules and the reduced action, specifically targeting the truncation of the nonlinear appearance of the scalar component of the Yang-Mills field in the base space. By imposing this truncated T-duality on the reduced action, we successfully determine the four-derivative bosonic couplings in the minimal basis, where field redefinition is imposed. Notably, these couplings, which are associated with the Lorentz Chern-Simons coupling $H\Omega$, exhibit an exact correspondence with the NS-NS couplings found in the Metsaev-Tseytlin action. Furthermore, we investigate the bosonic couplings in the maximal basis, where field redefinition is not imposed. In this scenario, the truncated T-duality fixes the effective action up to 17 arbitrary parameters. By assigning specific values to these parameters, we establish a framework in which the NS-NS couplings align with those in the Meissner action. Remarkably, within this scheme, the Yang-Mills couplings precisely coincide with those obtained through the S-matrix method.