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:
[1] | Charbonneau, Benoit and Hurtubise, Jacques, Singular {H}ermitian–{E}instein monopoles on the product of a circle and a {R}iemann surface, International Mathematics Research Notices. IMRN, 2011, 1, 175-216, (2011) · Zbl 1252.53036 · doi:10.1093/imrn/rnq059 |
[2] | Kontsevich, M. and Soibelman, Y., Riemann-Hilbert correspondence in dimension one, {F}ukaya categories and periodic monopoles · Zbl 1202.81120 |
[3] | Kronheimer, P. B., Monopoles and {T}aub-{NUT} metrics |
[4] | Mochizuki, Takuro, Periodic monopoles and difference modules · Zbl 1441.53016 |
[5] | Mochizuki, Takuro, Doubly-periodic monopoles and \(q\)-difference modules · Zbl 1441.53016 |
[6] | Mochizuki, Takuro and Yoshino, Masaki, Some characterizations of {D}irac type singularity of monopoles, Communications in Mathematical Physics, 356, 2, 613-625, (2017) · Zbl 1378.70028 · doi:10.1007/s00220-017-2981-z |
[7] | Simpson, Carlos T., Constructing variations of {H}odge structure using {Y}ang–{M}ills theory and applications to uniformization, Journal of the American Mathematical Society, 1, 4, 867-918, (1988) · Zbl 0669.58008 · doi:10.2307/1990994 |
[8] | Yoshino, Masaki, A {K}obayashi–{H}itchin correspondence between {D}irac-type singular mini-holomorphic bundles and {HE}-monopoles |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.