A bstract The open string sector of the topological Bmodel on CY ( m + 2)folds is described by m graded quivers with superpotentials. This correspondence generalizes the connection between CY ( m + 2)folds and gauge theories on the worldvolume of D(5 − 2 m )branes for m = 0 , . . . , 3 to arbitrary m . In this paper we introduce the CalabiYau product, a new algorithm that starting from the known quiver theories for a pair of toric CY m +2 and CY n +2 produces the quiver theory for a related CY m + n +3 . This method significantly supersedes existing ones, enabling the simple determination of quiver theories for geometries that were previously out of practical reach.
Fivedimensional SCFTs and gauge theory phases: an Mtheory/type IIA perspective
We revisit the correspondence between CalabiYau (CY) threefoldisolated singularities \mathbf{X} 𝐗 and fivedimensional superconformal field theories (SCFTs), which ariseat low energy in Mtheory on the spacetime transverse to \mathbf{X} 𝐗 .Focussing on the case of toric CY singularities, we analyze the“gaugetheory phases” of the SCFT by exploiting fiberwise Mtheory/typeIIA duality. In this setup, the lowenergy gauge group simply arises onstacks of coincident D6branes wrapping 2cycles in some ALE space oftype A_{M1} A M − 1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X} 𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs)can be read off systematically. Different type IIA “reductions” giverise to different gauge theory phases, whose existence depends on theparticular (partial) resolutions of the isolated singularity \mathbf{X} 𝐗 .We also comment on the case of nonisolated toric singularities.Incidentally, we propose a slightly modified expression for theCoulombbranch prepotential of 5d \mathcal{N}=1 𝒩 = 1 gauge theories.
 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10165541
 Journal Name:
 SciPost Physics
 Volume:
 6
 Issue:
 5
 ISSN:
 25424653
 Sponsoring Org:
 National Science Foundation
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