Abstract
We study the first-order in α′ corrections to 4-charge black holes (with the Reissner-Nordström black hole as a particular example) beyond the near-horizon limit in the Heterotic Superstring effective action framework. The higher-curvature terms behave as delocalized sources in the equations of motion and in the Bianchi identity of the 3-form. For some charges, this introduces a shift between their values measured at the horizon and asymptotically. Some of these corrections and their associated charge shifts, but not all of them, can be canceled using appropriate SU(2) instantons for the heterotic gauge fields. The entropy, computed using Wald’s formula, is in agreement with the result obtained via microstate counting when the delocalized sources are properly taken into account.
Highlights
Extremal, 4-charge black holes which will contain the first-order in α corrections to the heterotic version of the black holes whose microscopic entropy was computed and compared with the supergravity result in refs. [5,6,7]
We study the first-order in α corrections to 4-charge black holes beyond the near-horizon limit in the Heterotic Superstring effective action framework
The AdS3 and S3 factors are standard in the three-charge family of extremal black holes, and the quotient of the sphere by Zn is related to the presence of a charge-n KK monopole
Summary
We only need to know the metric and the two scalar fields of the 5dimensional solution (the 5-dimensional dilaton field φ and the Kaluza-Klein scalar that measures the radius of the 6 → 5 compactification, k). These are obtained from the 10dimensional metric and dilaton with the same relations used in absence of α corrections, [2], and read ds2 = f 2dt2 − f −1dσ , e2φ = e2φ∞ Z0 , Z−. We should mention that the SU(2) instanton fields have exactly the same expression as in 10 dimensions
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