Monopole condensation and confining phase of \(N=1\) gauge theories via M-theory fivebrane. (English) Zbl 0947.81110
Summary: 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.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
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