In order to test whether the microscopic entropy computed by string/(AdS/CFT) methodsmatches the macroscopic one for stringy black holes at higher orders in alpha’ it iscrucial to have a reliable computation of the latter. A prominent candidate is thequantity that plays the role of the entropy in the first law of black hole thermodynamicsfor any matter-free diff-invariant theory: the Wald entropy. Iyer and Wald gave a widelyused prescription to compute it when the matter fields are tensors. However, in the caseof the black-hole solutions of the heterotic superstring effective action to first orderin alpha’ the entropy obtained using this prescription fails to satisfy the first law.The main reason for this failure is the fact that most matter fields have gauge freedomsand, therefore, they are not tensors.In this talk I will show how to compute the diffeomorphism Noether charge (Wald entropy)by dealing correctly with the gauge freedoms of the matter fields. I will apply thismethodology to different theories including the heterotic superstring effective action tofirst order in alpha’. The resulting formula will be used to compute the alpha’corrections to the entropy of the several black-hole solutions of the heteroticsuperstring effective action to first order in alpha’.
