String Geometry Theory and The String Vacuum
arxiv(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.
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