  We investigate non-dilatonic p-branes in the near-extremal, near-horizon
regime. A two-dimensional gravity model, obtained from dimensional reduction,
gives an effective description of the brane. We show that the AdS_p+2/CFT_p+1
correspondence at finite temperature admits an effective description in terms
of a AdS_2/CFT_1 duality endowed with a scalar field, which breaks the
conformal symmetry and generates a non-vanishing central charge. The entropy of
the CFT_1 is computed using Cardy formula. Fixing in a natural way a free,
dimensionless, parameter introduced in the model by a renormalization
procedure, we find exact agreement between the CFT_1 entropy and the
Bekenstein-Hawking entropy of the brane.
