O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'

We perform the toroidal compactification of the full Bergshoeff-de Roo version of the Heterotic Superstring effective action to first orderin ${\alpha }^{\mathrm{\prime }}$. The dimensionally-reduced action is given in a manifestly-O(n,n)-invariant form which we use to derive a manifestly-O(n,n)-invariant Wald entropy formula which we then use to compute the entropy of ${\alpha }^{\mathrm{\prime }}$-corrected, 4-dimensional, 4-charge, static, extremal, supersymmetric black holes.