Chapter 12
Application to Superstring Theory
Abstract The last chapter describes an example of solving the inverse problem
of string theory as an application of deep learning. The superstring theory unifies
gravity and other forces, and in recent years, the “holographic principle,” that
the world governed by gravity is equivalent to the world of other forces, has
been actively studied. We will solve the inverse problem of the emergence of the
gravitational world by applying the correspondence to the dynamical system seen in
Chap. 9, and look at the new relationship between machine learning and spacetime.
Superstring theory has been studied as quantum theory of gravity and as a theory
that can describe all the forces in the universe in a unified way. 1 This chapter shows
examples of applying machine learning, especially deep learning, to mathematical
problems in string theory. Despite its history, a variety of studies that apply machine
learning techniques to physics in earnest has only recently opened up. The content
of this chapter is mainly based on collaborative research between the authors and
Sotaro Sugishita [118, 130], and other kinds of research on string theory have been
done, so diverse progress is expected.
First, let us outline two of the inverse problems in string theory from a general
perspective without using mathematical formulas. Next, we explain how to regard
deep neural networks as spacetimes, as one of the methods to solve an inverse
problem in the holographic principle.
12.1 Inverse Problems in String Theory
There are two major characteristics of the mathematical achievements of superstring
theory that enable the quantization of gravity. The first is the constraint that the
spacetime needs to be 10-dimensional, and the second is that it results in various
gauge symmetries and sets of elementary particles which transform under them.
1 For an introductory book on string theory, see [129].
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. Tanaka et al., Deep Learning and Physics, Mathematical Physics Studies,
https://doi.org/10.1007/978-981-33-6108-9_12
173
Application to Superstring Theory
Abstract The last chapter describes an example of solving the inverse problem
of string theory as an application of deep learning. The superstring theory unifies
gravity and other forces, and in recent years, the “holographic principle,” that
the world governed by gravity is equivalent to the world of other forces, has
been actively studied. We will solve the inverse problem of the emergence of the
gravitational world by applying the correspondence to the dynamical system seen in
Chap. 9, and look at the new relationship between machine learning and spacetime.
Superstring theory has been studied as quantum theory of gravity and as a theory
that can describe all the forces in the universe in a unified way. 1 This chapter shows
examples of applying machine learning, especially deep learning, to mathematical
problems in string theory. Despite its history, a variety of studies that apply machine
learning techniques to physics in earnest has only recently opened up. The content
of this chapter is mainly based on collaborative research between the authors and
Sotaro Sugishita [118, 130], and other kinds of research on string theory have been
done, so diverse progress is expected.
First, let us outline two of the inverse problems in string theory from a general
perspective without using mathematical formulas. Next, we explain how to regard
deep neural networks as spacetimes, as one of the methods to solve an inverse
problem in the holographic principle.
12.1 Inverse Problems in String Theory
There are two major characteristics of the mathematical achievements of superstring
theory that enable the quantization of gravity. The first is the constraint that the
spacetime needs to be 10-dimensional, and the second is that it results in various
gauge symmetries and sets of elementary particles which transform under them.
1 For an introductory book on string theory, see [129].
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. Tanaka et al., Deep Learning and Physics, Mathematical Physics Studies,
https://doi.org/10.1007/978-981-33-6108-9_12
173