Abstract
In Witten's topological theory of the generation problem, gauge groups are identified with theE 8 centraliser of the holonomy group of the internal manifold. Here we show that this amounts to interpreting gauge groups as generalised symmetry groups of the (internal) Levi-Civitá connection. We then give techniques for computing centralisers in exceptional groups, taking into account the fact that holonomy groups are frequently disconnected. These techniques allow us to deal with compact locally irreducible Ricci-flat Riemannian manifolds of all holonomy types and dimensions.
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Communicated by S.-T. Yau
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McInnes, B. Gauge theory in Witten's approach to the generation problem. Commun.Math. Phys. 138, 107–136 (1991). https://doi.org/10.1007/BF02099671
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DOI: https://doi.org/10.1007/BF02099671