Supersymmetric index of the M-theory 5-brane and little string theory

We propose a six-dimensional framework to calculate the supersymmetric inde x of M-theory 5-branes wrapped on a six-manifold with product topology M-4 x T-2, where M-4 is a holomorphic 4-cycle in a Calabi-Yau three-fold. This is obtained by zero-modes counting of the self-dual tensor contribution plu s "little" string states and correctly reproduces the known results which c an be obtained by shrinking or blowing the T-2 volume parameter. We also ex tract the geometric moduli space of the multi M5-brane system and infer the generic structure of the supersymmetric index for more general geometries. (C) 2001 Elsevier Science B.V. All rights reserved.