Small black holes in the large D limit

A bstract The large D limit of AdS 2 × S D −2 solutions in the particular higher-derivative Lovelock-type theory is analyzed. The theory and the solutions were originally considered in an attempt to effectively describe near-horizon behavior of D -dimensional spherically symmetric 2-charge small extremal black holes which in superstring theory context are assumed to correspond to configurations in S 1 × T 9− D compactification schemes in which fundamental string is wound around circle S 1 . Though in D → ∞ limit the action contains infinite number of higher-derivative terms, their contributions to equations of motion sum into simple exponential form which allows us to find explicit solutions. A simplicity of this example gives us the opportunity to study some connections between α ′ and 1 /D expansions. In the leading order in 1 /D the relation between the string parameter α ′ and the radius of the horizon r h (in the string frame) satisfies r h ∝ , i.e., we obtain an explicit realization of the relation inferred by Emparan et al. in the different context of large black holes in the ordinary Einstein gravity where α ′ is not manifestly present.