Triply periodic monopoles and difference modules on elliptic curves. (English) Zbl 1441.53016
Summary: We explain the correspondences between twisted monopoles with Dirac type singularity and polystable twisted mini-holomorphic bundles with Dirac type singularity on a 3-dimensional torus. We also explain that they are equivalent to polystable parabolic twisted difference modules on elliptic curves.
MSC:
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 14H52 | Elliptic curves |
Keywords:
twisted monopoles; twisted difference modules; twisted mini-holomorphic bundles; Kobayashi-Hitchin correspondenceReferences:
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