Abstract
We study the first-order in α′ corrections to non-extremal 4-dimensional dyonic Reissner-Nordström (RN) black holes with equal electric and magnetic charges in the context of Heterotic Superstring effective field theory (HST) compactified on a T6. The particular embedding of the dyonic RN black hole in HST considered here is not supersymmetric in the extremal limit. We show that, at first order in α′, consistency with the equations of motion of the HST demands additional scalar and vector fields become active, and we provide explicit expressions for all of them. We determine analytically the position of the event horizon of the black hole, as well as the corrections to the extremality bound, to the temperature and to the entropy, checking that they are related by the first law of black-hole thermodynamics, so that ∂S/∂M = 1/T. We discuss the implications of our results in the context of the Weak Gravity Conjecture, clarifying that entropy corrections for fixed mass and charge at extremality do not necessarily imply corrections to the extremal charge-to-mass ratio.
Highlights
Only be considered good ST solutions if one can prove that taking into account the terms of higher order in α only introduces small corrections in the solutions
We study the first-order in α corrections to non-extremal 4-dimensional dyonic Reissner-Nordstrom (RN) black holes with equal electric and magnetic charges in the context of Heterotic Superstring effective field theory (HST) compactified on a T 6
In this paper we have computed the first-order in α corrections to a dyonic Reissner-Nordstrom black hole explicitly embedded in the Heterotic String Theory
Summary
Our starting point is a zeroth-order in α solution of the 10-dimensional Heterotic Superstring effective field theory (HST) given by the following 10-dimensional fields, which we distinguish from the 4-dimensional ones by the hats:. The rest of the 4-dimensional fields which are active include, apart from the dilaton e−φ and the Kaluza Klein scalar k that we have mentioned above, a Kaluza-Klein vector field Aμ, a winding vector field Bμ and a Kalb-Ramond 2-form Bμν that, in 4-dimensions, can be traded by an axion field that we are going to denote by χ. They take much more complicated forms than the metric, with logarithmic divergences at r = r−. This is in agreement with previous computations of corrections in uncharged solutions [9,10,11, 13, 14]
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