PoS - Proceedings of Science
Volume 463 - Corfu Summer Institute 2023 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2023) - Workshop on Noncommutative and Generalized Geometry in String Theory, Gauge Theory and Related Physical Models
String Geometry Theory and The String Vacuum
M. Sato
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Published on: July 31, 2024
Abstract
String geometry theory is a candidate of the non-perturvative formulation of string theory. In this theory, strings constitute not only particles but also the space-time. In this review, we identify perturbative vacua, and derive the path-integrals of all order perturbative strings on the corresponding string backgrounds by considering the fluctuations around the vacua. On the other hand, the most dominant part of the path-integral of string geometry theory is the zeroth order part in the fluctuation of the action, which is obtained by substituting the perturbative vacua to the action. This part is identified with the effective potential of the string backgrounds and obtained explicitly. The global minimum of the potential is the string vacuum. The urgent problem is to find the global minimum. We introduce both analytical and numerical methods to solve it. Especially, we analyze a generic region of the potential where the internal space is a torus. As a result, we find that the potential is bounded below and has the minimum in the region where non-trivial fluxes are determined. This fact supports that our approach is right.
DOI: https://doi.org/10.22323/1.463.0261
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