Abstract
We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c − a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.
Highlights
The aim of the swampland program [1] is to understand what subset of the infinite space of possible effective field theories can arise at low energies from theories of quantum gravity
We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordstrom black holes for general dimensions and horizon geometries
One fruitful source of such IR intuition is the physics of black holes, which are believed to conform to general relativity and the laws of black hole thermodynamics in the semiclassical regime
Summary
The aim of the swampland program [1] is to understand what subset of the infinite space of possible effective field theories can arise at low energies from theories of quantum gravity. This requires finding simple criteria for classifying these theories; those that admit UV completions including quantum gravity are in the landscape, and those that do not are in the swampland. One that has attracted considerable interest is the Weak Gravity Conjecture (WGC), which roughly states that there are states whose mass is smaller than their charge [3] — they are states for which “gravity is the weakest force.” Such states are labelled “superextremal,” and may be provided by fundamental particles or non-perturbative states such as black holes. These black holes are believed to obey an “extremality bound” on its mass to charge ratio,
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