Abstract
We study the distance in the space of couplings of two-dimensional quantum field theories, as specified by the Zamolodchikov metric. We show that for world-sheet supersymmetric theories, the Witten index (target space Euler number) cannot be changed while moving a finite distance, and illustrate this for N = 1 and N = 2 minimal series as well as for Calabi-Yau manifolds.
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