T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in ${\alpha }^{\prime }$

Abstract

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter ${\alpha }^{\prime }$ and re-derive the ${\alpha }^{\prime }$-corrected Buscher rules first found in arXiv:hep-th/9506156 , proving the T duality invariance of the dimensionally-reduced action to that order in ${\alpha }^{\prime }$. 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 ${\alpha }^{\prime }$-corrected T duality transformations. This formula has been successfully applied to ${\alpha }^{\prime }$-corrected 4-dimensional non-extremal Reissner-Nordström black holes in arXiv:1910.14324 and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.

Misprints in intermediate equations corrected in agreement with the erratum submitted to the journal. Final results not affected

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