396 research outputs found
Phases of Five-dimensional Theories, Monopole Walls, and Melting Crystals
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
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.Comment: 45 pages, 11 figure
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