A comprehensive survey of brane tilings

作者:Franco, Sebastian*; He, Yang-Hui; Sun, Chuang; Xiao, Yan
来源:International Journal of Modern Physics A, 2017, 32(23-24): 1750142.
DOI:10.1142/S0217751X17501421

摘要

An infinite class of 4d N = 1 gauge theories can be engineered on the worldvolume of D3-branes probing toric Calabi-Yau 3-folds. This kind of setup has multiple applications, ranging from the gauge/gravity correspondence to local model building in string phenomenology. Brane tilings fully encode the gauge theories on the D3-branes and have substantially simplified their connection to the probed geometries. The purpose of this paper is to push the boundaries of computation and to produce as comprehensive a database of brane tilings as possible. We develop efficient implementations of brane tiling tools particularly suited for this search. We present the first complete classification of toric Calabi-Yau 3-folds with toric diagrams up to area 8 and the corresponding brane tilings. This classification is of interest to both physicists and mathematicians alike.