NONCRITICAL BOSONIC STRING CORRECTIONS TO THE BLACK-HOLE ENTROPY

We calculate the quantum corrections to the entropy of a very large black hole, coming from the theory of a D-dimensional, noncritical bosonic string. We show that for D > 2, as a result of modular invariance the entropy is uv finite though it diverges in the ir (while for D = 2 the entropy contains both uv and ir divergences). The issue of modular invariance in field theory, in connection with black hole entropy, is also investigated.