Unveiling the mysteries of the E-string with Calabi-Yau geometry

The E-string theory is usually considered as the simplest among 6D (1,0) superconformal field theories. Nonetheless, we still have little information about its spectrum of operators. In this talk, I'm going to describe our recent geometric approach using F-theory compactification on an elliptic Calabi-Yau threefold. The elliptic fibration is non-flat, which means that there are complex surface components in the fiber direction. From the geometry of non-flat fiber, we read out an infinite tower of particle states in the E-string theory. I will also discuss its relevance to 4D standard model building, which is a main motivation of this work.