Monopoles, affine algebras and the gluino condensate

By N. Davies, T. Hollowood, V. Khoze. 2000

151 citations recorded by the source corpus.

We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly coupled way for a small radius. The dominant contributions to the path integral on the cylinder arise from magnetic monopoles which play the role of instanton constituents. We find that the semi-classically generated superpotential of the theory is the affine Toda potential for an associated twisted affine algebra. We determine the supersymmetric vacua and calculate the values of the gluino condensate. The number of supersymmetric vacua is equal to c2, the dual Coxeter number, and in each vacuum the monopoles carry a fraction 1/c2 of topological charge. As the results are independent of the radius of the circle, they are also valid in the strong coupling regime where the theory becomes decompactified. For gauge groups SU(N), SO(N) and ...

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6c495872a74db061979cb0f97df78ad6717deace

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In Geometry and Topology

1. E. Poppitz
2. T. Schäfer
3. P. Argyres
4. M. Unsal

In Nuclear and High Energy Physics

1. M. Unsal
2. P. Argyres
3. E. Poppitz
4. T. Schäfer
5. G. Dunne
6. Daniele Dorigoni
7. Yuji Tachikawa
8. A. Cherman

Citations in the corpus

• M theory and singularities of exceptional holonomy manifolds (2004, unknown): “This exactly mimics the strategy of [106] in field theory.”
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, methodology): “The remainder of this section reviews, following [14, 50], the elementary semiclassical configurations, and derives the first order corrections to the effective Lagrangian.”
• Continuity, deconfinement, and (super) Yang-Mills theory (2012, methodology): “We recall again that f is nonzero only away from the center-symmetric point, thus the extremal point of W (B), B = 0, still corresponds to the center-symmetry preserving vacuum b′ = 0, in accord with the conclusions from the earlier work [12,40].”