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arXiv · 1402.7117

Phases of Five-dimensional Theories, Monopole Walls, and Melting Crystals

Sergey A. Cherkis
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Abstract

Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperk\"ahler; 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 $\mathbb{R}^3\times T^2$ 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.

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Sergey A. Cherkis. 2014-02-28. Phases of Five-dimensional Theories, Monopole Walls, and Melting Crystals. https://doi.org/10.1007/jhep06(2014)027

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