Abstract
= 1 supersymmetric U(N) gauge theory with
adjoint matter Φ and a polynomial superpotential Tr W(Φ)
has been much studied recently. The classical theory has several vacua
labeled by integers (N1, N2, ..., Nk), with the classical
unbroken gauge group ∏iU(Ni). Quantum mechanically, each
classical vacuum leads to ∏iNi different vacua. As the
parameters of W(Φ) are varied, these vacua change in a continuous
(and holomorphic) fashion. We find that vacua associated with
(N1, N2, ..., Nk) can be continuously transformed to vacua with
(Ñ1, Ñ2, ..., Ñk), thus leading
to a new kind of duality. Traditional order parameters, like the
Wilson loop and 't Hooft loop, sometimes distinguish different phases.
We also find phases that are not distinguished by conventional order
parameters. The whole picture of the phase diagram is reminiscent of
the phase diagram of M-theory.
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