Two-charge small black hole entropy: String-loops and multi-strings

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We investigate the inclusion of 10-dimensional string loop corrections to the entropy function of two-charge extremal small black holes of the heterotic string theory compactified on S¹ x T⁵ and show that the entropy is given by π√a q₁ q₂+b q₁ where q₁ and q₂ are the charges with q₁ >> q₂ >> 1 and a and b are constants. Incorporating certain multi-string states into the microstate counting, we show that the new statistical entropy is consistent with the macroscopic scaling for one and two units of momentum (winding) and large winding (momentum). We discuss our scaling from the point of view of related AdS₃ central charge and counting of chiral primaries in superconformal quantum mechanics as well.