Kähler potential and higher derivative terms from M-theory fivebrane

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 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.

The off-shell M5-brane and non-perturbative gauge theory

“…We will also discuss how the superpotential arises from the kinetic term for the scalars in the (2,0) theory living on the world-volume of the fivebrane via deconstruction. This generalizes the relation between the (2,0) theory and N = 2 SYM [14,12] to the case of N = 1, and in particular to the precise computation of the F-terms.…”

“…For M5-brane configurations with N = 2 supersymmetry, where only one of the scalars t or w is active, it is well known [12,14] that the equations of motion for the gauge fields on the 5-brane correctly reproduce the Kähler potential of the N = 2 SYM theory. It is interesting to see in detail whether this relation generalizes to the N = 1 case.…”

“…It would be interesting to understand the gauge theory resolvent more directly from the fivebrane point of view. Let us next consider the Kähler potential of the low-energy effective theory on the five-branes, as considered in [12,14]. We will mostly follow the computation of [12].…”

On non-commutative super Yang–Mills

“…In the type IIA picture discussed below, the D4 branes end on the NS5 branes at the positions a i and u 0 is proportional to their center-of-mass position. The kinetic term if the effective action can be written as [34] …”

Hyperelliptic integrable systems on K3 and rational surfaces

“…As noted by Nakatsu et al [18] and de Boer et al [19], the Seiberg-Witten curves are cut out from X by the equation…”