5-DIMENSIONAL SUPERSYMMETRIC GAUGE-THEORIES AND DEGENERATIONS OF CALABI-YAU SPACES

We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon inc luding a Wess-Zumino type Chem-Simons term. We discuss some necessary conditions for existence of non-trivial renormalization group fixed po ints and find all possible gauge groups and matter content which satis fy them. In some cases, the existence of these fixed points can be inf erred from string duality considerations. In other cases, they arise f rom M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with non-trivial fixed points is a fairly complete classification of a class of singularities of Calabi -Yau threefolds which generalize the ''del Pezzo contractions'' and oc cur at higher codimension walls of the Kahler cone. (C) 1997 Elsevier Science B.V.