Small black holes in the large D limit

The large D limit of AdS(2) x SD-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 x T9-D compactification schemes in which fundamental string is wound around circle S-1. Though in D -> infinity 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 alpha' and 1/D expansions. In the leading order in 1/D the relation between the string parameter alpha' and the radius of the horizon r(h) (in the string frame) satisfies r(h) proportional to D root alpha', 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 alpha' is not manifestly present.