The dilaton potential from N=1

Recent understanding of N = 1* supersymmetric theory (mass deformed N = 4) has made it possible to find an exact superpotential which encodes the prop erties of the different phases of the theory. We consider this superpotenti al as an illustrative example for the source of a nontrivial scalar potenti al for the string theory dilaton and study its properties. The superpotenti al is characterized by the rank of the corresponding gauge group (N) and in tegers p,q,k labelling the different massive phases of the theory, For gene ric values of these parameters, we find the expected runaway behaviour of t he potential to vanishing string coupling. But there are also supersymmetri c minima at weak coupling stabilizing the dilaton field. An interesting pro perty of this potential is that there is a proliferation of supersymmetric vacua in the confining phases. with the number of vacua increasing with N a nd leading to a kind of staircase potential. For a range of parameters, it is possible to obtain realistic values for the gauge coupling. (C) 2001 Els evier Science B.V. All rights reserved.