The Geometry of GTPs and 5d SCFTs
arxiv(2024)
摘要
We make progress in understanding the geometry associated to the Generalized
Toric Polygons (GTPs) encoding the Physics of 5d Superconformal Field Theories
(SCFTs), by exploiting the connection between Hanany-Witten transitions and the
mathematical notion of polytope mutations. From this correspondence, it follows
that the singular geometry associated to a GTP is identical to that obtained by
regarding it as a standard toric diagram, but with some of its resolutions
frozen in way that can be determined from the invariance of the so-called
period under mutations. We propose the invariance of the period as a new
criterion for distinguishing inequivalent brane webs, which allows us to
resolve a puzzle posed in the literature. A second mutation invariant is the
Hilbert Series of the geometry. We employ this invariant to perform
quantitative checks of our ideas by computing the Hilbert Series of the BPS
quivers associated to theories related by mutation. Lastly, we discuss the
physical interpretation of a mathematical result ensuring the existence of a
flat fibration over ℙ^1 interpolating between geometries connected
by mutation, which we identify with recently introduced deformations of the
corresponding BPS quivers.
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