Tsukuba, Japan—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, we mathematically investigated whether the behavior of space B also has the same properties as that of space A. We 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 we made some assumptions to prove this theorem, in the future, we will clarify whether this theorem holds even without these assumptions.

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This work was supported by NSFC, No.12031017, JSPS KAKENHI Grant Number 18K13415, and Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849).

_{Original Paper}

Title of original paper:

An ε-regularity theorem for line bundle mean curvature flow

Journal:

*The Asian Journal of Mathematics*

DOI:

10.4310/AJM.2022.v26.n6.a1

_{Correspondence}

Associate Professor YAMAMOTO, Hikaru

Institute of Pure and Applied Science, University of Tsukuba

_{Related Link}

Institute of Pure and Applied Sciences

#### Journal

Asian Journal of Mathematics

#### Article Title

An ε-regularity theorem for line bundle mean curvature flow

#### Article Publication Date

27-Apr-2023