Abstract
Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperkähler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their moduli spaces can be identified, on the one hand, with Coulomb branches of five-dimensional supersymmetric quantum field theories on $ \mathbb{R} $ 3 × T 2 and, on the other hand, with moduli spaces of local Calabi-Yau metrics on the canonical bundle of a del Pezzo surface. We explore the asymptotic metric of these moduli spaces and compare our results with Seiberg’s low energy description of the five-dimensional quantum theories. We also give a natural description of the phase structure of general monowall moduli spaces in terms of triangulations of Newton polygons, secondary polyhedra, and associahedral projections of secondary fans.
Highlights
Doubly-periodic Monopoles for Yang-Mills fields or its dimensional reductions
Moduli spaces of doubly periodic monopoles, called monopole walls or monowalls, are hyperkahler; when four-dimensional, they are self-dual gravitational instantons
We explore the asymptotic metric of these moduli spaces and compare our results with Seiberg’s low energy description of the five-dimensional quantum theories
Summary
Called a monopole wall, as defined in [13]. In physical terms considering the Yang-Mills-Higgs theory with the action. If the gauge group U(n) is completely broken by the Higgs field outside of some ball, one expects one set of magnetic fluxes to the right of the ball, and possibly different set of magnetic fluxes to the left of the ball. This is the monopole wall, or the monowall. Monowall is a domain wall separating two regions with Higgs broken gauge group and different constant magnetic field. We identify phases in the parameter space which distinguish different monowall dynamics
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