Kahler Potential and Higher Derivative Terms from M Theory Fivebrane

TL;DR

This paper investigates non-holomorphic quantities in M theory fivebrane constructions of 4D supersymmetric gauge theories, comparing supergravity results with field theory expectations, and computes metrics on Higgs branches with partial agreement.

Contribution

It provides the first detailed computation of non-holomorphic quantities and Higgs branch metrics from M theory fivebrane configurations, highlighting where supergravity matches or diverges from gauge theory.

Findings

Kahler potential for N=2 Coulomb branch is correctly reproduced.

Higher derivative terms differ from gauge theory expectations.

Higgs branch metrics show agreement with gauge theory results.

Abstract

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 Kahler 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 Kahler 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.