Unsupervised Machine Learning Techniques for Exploring Tropical
  Coamoeba, Brane Tilings and Seiberg Duality
Rak-Kyeong Seong
We introduce unsupervised machine learning techniques in order to identify
toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same
toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are
worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are
realized in terms of a Type IIB brane configuration known as a brane tiling. It
corresponds to the skeleton graph of the coamoeba projection of the mirror
curve associated to the toric Calabi-Yau 3-fold. When we vary the complex
structure moduli of the mirror Calabi-Yau 3-fold, the coamoeba and the
corresponding brane tilings change their shape, giving rise to different toric
phases related by Seiberg duality. We illustrate that by employing techniques
such as principal component analysis (PCA) and t-distributed stochastic
neighbor embedding (t-SNE), we can project the space of coamoeba labelled by
complex structure moduli down to a lower dimensional phase space with phase
boundaries corresponding to Seiberg duality. In this work, we illustrate this
technique by obtaining a 2-dimensional phase diagram for brane tilings
corresponding to the cone over the zeroth Hirzebruch surface F0.