Monopole Condensation and Confining Phase of N=1 Gauge Theories Via M Theory Fivebrane

TL;DR

This work uses the M theory fivebrane to study confining phase $N=1$ gauge theories, showing how monopole (dyon) condensation on singular loci of the $N=2$ moduli space yields confinement and a mass gap. By constructing explicit brane configurations and comparing with field-theoretic analyses, it demonstrates exact agreement for dyon vevs and, for $SU(2)$, meson vevs, while revealing discrepancies for higher-rank enhanced gauge groups that imply nonzero $W_ ext{Delta}$ in the integrating-in framework. The paper also explores Landau–Ginzburg type deformations, potential nontrivial fixed points, and the emergence of baryonic/non-baryonic Higgs branches from brane geometry, offering a rich geometric perspective on nonperturbative dynamics. Overall, the brane geometry provides both a check on holomorphic field theory data and a pathway to uncovering new structure beyond the standard $N=2 o N=1$ perturbative analysis, with implications for fixed points and dualities in four-dimensional supersymmetric theories.

Abstract

The fivebrane of M theory is used in order to study the moduli space of vacua of confining phase N=1 supersymmetric gauge theories in four dimensions. The supersymmetric vacua correspond to the condensation of massless monopoles and confinement of photons. The monopole and meson vacuum expectation values are computed using the fivebrane configuration. The comparison of the fivebrane computation and the field theory analysis shows that at vacua with a classically enhanced gauge group SU(r) the effective superpotential obtained by the "integrating in" method is exact for r=2 but is not exact for r > 2. The fivebrane configuration corresponding to N=1 gauge theories with Landau-Ginzburg type superpotentials is studied. N=1 non-trivial fixed points are analyzed using the brane geometry.

Figures (1)

• Figure 1: The Dyon and Meson Vevs in the Brane Geometry