KAHLER POTENTIAL AND HIGHER-DERIVATIVE TERMS FROM M-THEORY FIVEBRANE

The construction of four-dimensional supersymmetric gauge theories via the fivebrane of M-theory wrapped around a Riemann surface has been s uccessfully applied to the computation of holomorphic quantities of fi eld theory. In this paper we compute non-holomorphic quantities in the eleven-dimensional supergravity limit of M-theory. While the Kahler p otential on the Coulomb of N = 2 theories is correctly reproduced, hig her derivative terms in the N = 2 effective action differ from what is expected for the four-dimensional gauge theory. For the Kahler potent ial of N = 1 theories at an abelian Coulomb phase, the result again di ffers from what is expected for the four-dimensional gauge theory. Usi ng a gravitational back-reaction method for the fivebrane we compute t he metric on the Higgs branch of N = 2 gauge theories. Here we find an agreement with the results expected for the gauge theories. A similar computation of the metric on N = 1 Higgs branches yields information on the complex structure associated with the flavor rotation in one ca se and the classical metric in another. We discuss what four-dimension al field theory quantities can be computed via the fivebrane in the su pergravity limit of M-theory. (C) 1998 Elsevier Science B.V.