T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter alpha ' and re-derive the alpha ' -corrected Buscher rules first found in ref. [42], proving the T duality invariance of the dimensionally-reduced action to that order in alpha '. We use Iyer and Wald's prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the alpha ' -corrected T duality transformations. This formula has been successfully applied to alpha ' -corrected 4-dimensional non-extremal Reissner-Nordstrom black holes in ref. [21] and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.