In the realm of theoretical physics, superstring theories propose the existence of parallel worlds (A-side and B-side). Although it’s impossible to differentiate between these universes, they are interlinked. A team of researchers at the University of Tsukuba have demonstrated through mathematical evidence that under specific circumstances, dramatic transformations (“blowing up”) which do not transpire within the A-side, similarly do not occur within the B-side.
Theoretical string theory in theoretical physics predicts the existence of parallel worlds (mirror symmetry prediction). These two worlds (A-side and B-side) are supposed to differ in terms of the six-dimensional spaces (A and B) hidden in each world. However, as these spaces are extremely similar and invisible, theoretically, we cannot distinguish the world that we live in. Considerable research has been conducted on the properties of space A, and extreme changes (i.e., blowing up) do not occur in it under certain conditions.
However, recently it has been discovered that spaces A and B are transformed in a certain way and their apparently different objects correspond to each other. However, the nature and extent of this transformation are not well understood, and research on the properties of space B has not yet progressed. In this study, the scientists mathematically investigated whether the behavior of space B also has the same properties as that of space A. They transferred a known phenomenon from the A-side to the B-side and proved that no blowing up occurs even in space B under certain conditions.
This achievement provides mathematical proof for one of the previously intuitively expected similarities between A-side and B-side. Although the researchers made some assumptions to prove this theorem, in the future, they will clarify whether this theorem holds even without these assumptions.
Reference: “An ε-regularity theorem for line bundle mean curvature flow” by Xiaoli Han and Hikaru Yamamoto, 27 April 2023, The Asian Journal of Mathematics.