Lovelock type gravity and small black holes in heterotic string theory

We analyze near horizon behavior of small D-dimensional 2-charge black holes by modifying tree level effective action of heterotic string with all extended Gauss-Bonnet densities. We show that there is a nontrivial and unique choice of parameters, independent of D, for which the black hole entropy in any dimension is given by 4π(nw)1/2, which is exactly the statistical entropy of 1/2-BPS states of heterotic string compactified on T9-D × S1 with momentum n and winding w. This, in a sense, extends the results of Sen JHEP07(2005)073 to all dimensions. We also show that our Lovelock type action belongs to the more general class of actions sharing the simmilar behaviour on the AdS2 × SD-2 near horizon geometry