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Graded Calabi Yau Algebras of dimension 3
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Graded Calabi Yau Algebras of dimension 3
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In this paper we prove that Graded Calabi Yau Algebras of dimension 3 are isomorphic to path algebras of quivers with relations derived from a superpotential. We show that for a given quiver $Q$ and a degree $d$, the set of good superpotentials of degree $d$, i.e. those that give rise to Calabi Yau algebras is either empty or almost everything (in the measure theoretic sense). We also give some constraints on the structure of quivers that allow good superpotentials, and for the simplest quivers we give a complete list of the degrees for which good superpotentials exist.
Forward citations
Cited by 2 Pith papers
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On the Origin of Toric Diagrams
A field's scaling dimension equals the number of perfect matchings at the chosen origin that contain it, making the gauge-theory Hilbert series equal the Ehrhart series of the dual polytope.
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Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
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