1206.3701 (Siddharth Dwivedi et al.)

Partial resolution of complex cones over Fano {\cal B}    [PDF]

Siddharth Dwivedi, P. Ramadevi

In our recent paper arXiv:1108.2387, we systematized inverse algorithm to obtain quiver gauge theory living on the M2-branes probing the singularities of special kind of Calabi-Yau four-folds which were complex cones over toric Fano $P^3$, ${\cal B}_1, {\cal B}_2, {\cal B}_3.$ These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data of $C^4$, orbifolds of $C^4$ and $P^3$ can be embedded inside the toric data of Fano {\cal B}. This method indirectly justifies that the two node quiver Chern-Simons theories corresponding to $C^4$, orbifolds of $C^4$ and $P^3$ can be obtained by higgsing matter fields of the three node parent quiver corresponding to Fano {\cal B} three-folds.

View original: http://arxiv.org/abs/1206.3701