Chern-Simons: Fano and Calabi-Yau
Amihay Hanany, Yang-Hui He
TL;DR
This paper classifies all smooth toric Fano threefolds and explores their relevance in brane-tilings and Chern-Simons theories related to M2-branes probing Calabi-Yau fourfold singularities.
Contribution
It provides a complete classification of smooth toric Fano threefolds and initiates analysis of their applications in brane-tilings and Chern-Simons theories.
Findings
Classification of 18 smooth toric Fano threefolds
Preliminary analysis of brane-tilings on these spaces
Potential importance in Calabi-Yau fourfold studies
Abstract
We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane-tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counter-parts: the del Pezzo surfaces.
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