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 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. © 2014 The Author(s).
CITATION STYLE
Cherkis, S. A. (2014). Phases of five-dimensional theories, monopole walls, and melting crystals. Journal of High Energy Physics, 2014(6). https://doi.org/10.1007/JHEP06(2014)027
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