Abstract
In previous works (arXiv:1610.07916, arXiv:1711.07921, arXiv:1807.00186) we studied a class of toric Calabi-Yau threefolds which engineer six-dimensional supersymmetric gauge theories with gauge group $U(N)$ and adjoint matter. The K\"ahler moduli space of these manifolds can be extended through flop transformations to include regions which are described by so-called shifted toric web diagrams. In this paper we analyse gauge theories that are engineered by these shifted toric web diagrams and argue that in specific limits, some of the them engineer five-dimensional quiver gauge theories with gauge group $G\subset U(N)$ and with fundamental and bi-fundamental matter. We discuss several examples in detail and describe how the matter sector is obtained from the six-dimensional parent theory.
Highlights
The engineering of five- and six-dimensional superconformal theories in string theory, using branes or geometry, has provided insights into various properties of these theories including the allowed matter content
High Energy Phys. 11 (2018) 016], we studied a class of toric Calabi-Yau threefolds which engineer six-dimensional supersymmetric gauge theories with gauge group UðNÞ and adjoint matter
This geometry engineers a five-dimensional gauge theory, which has been previously studied in the literature [36]: It corresponds to a theory with gauge group Uð3Þ whose matter content transforms as four copies of its fundamental representation
Summary
The engineering of five- and six-dimensional superconformal theories in string theory, using branes or geometry, has provided insights into various properties of these theories including the allowed matter content. The remaining web diagram (shown in Fig. 5) is still toric and, corresponds to local dP3 The latter engineers [36] a five-dimensional gauge theory with gauge group SUð2Þ and whose matter content transforms as Nf 1⁄4 2 copies of the fundamental representation. This geometry engineers a five-dimensional gauge theory, which has been previously studied in the literature [36]: It corresponds to a theory with gauge group Uð3Þ whose matter content transforms as four copies of its fundamental representation. The additional constraint relates the two coupling constants of the gauge groups
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