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*D. Kutasov*

Enrico Fermi Institute and

Department of Physics

University of Chicago

Chicago, IL 60637, USA

.2in

*A. Schwimmer*

Department of Physics of Complex Systems

Weizmann Institute of Science

Rehovot, 76100, Israel

.2in

*N. Seiberg*

Department of Physics and Astronomy

Rutgers University

Piscataway, NJ08855, USA

.3cm

We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between them depends on non-trivial facts about polynomial equations, i.e. singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges “trivial” classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.

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