Kähler 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 successfully applied to the computation of holomorphic quantities of field theory. In this paper we compute non-holomorphic quantities in the eleven-dimensional supergravity limit of M-theory. While the Kähler potential on the Coulomb of N = 2 theories is correctly reproduced, higher derivative terms in the N = 2 effective action differ from what is expected for the four-dimensional gauge theory. For the Kähler potential of N = 1 theories at an abelian Coulomb phase, the result again differs from what is expected for the four-dimensional gauge theory. Using a gravitational back-reaction method for the fivebrane we compute the 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 case and the classical metric in another. We discuss what four-dimensional field theory quantities can be computed via the fivebrane in the supergravity limit of M-theory.