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Quantum Gravity Beyond the End of the World

Wei, Zixia 京都大学 DOI:10.14989/doctor.k24403

2023.03.23

概要

As one of the most ancient subjects, the aim of theoretical physics is clear and simple. Theoretical physicists attempt to use languages as simple as possible to explain their observations
of nature, describe how the universe runs, and efficiently make correct predictions of the
real world. Such a language turns out to be a theoretical model. Since we only have one
real world, or at least we usually assume so, the developments of theoretical physics usually
come along with unifications of different models into a new one that consistently includes old
ones. The unification of gravity and spacetime curvature into general relativity by Einstein
is a good example. General relativity, together with quantum theory, are two of the most
important ingredients in modern physics established in the early 20th century.
In the theoretical physics of the 21st century, one of the most important yet challenging
problems is to construct a theory of quantum gravity, which is a unification of quantum
theory and gravity described by general relativity, and give testable predictions from it.
Nowadays, the holographic principle [1, 2] plays a significant role in the studies of quantum
gravity. The holographic principle states that a theory of quantum gravity, even though we
do not know how to precisely describe it, should be equivalent to a lower dimensional nongravitational quantum theory. The most well-studied example is the equivalence between
quantum gravity in a (d + 1)-dimensional asymptotically anti-de Sitter spacetime (AdS) and
a d-dimensional conformal field theory (CFT) living on its boundary, the so-called AdS/CFT
correspondence [3]. Here, AdS is a spacetime with a negative cosmological constant, and
CFT is a class of quantum theory that describes certain many-body systems. Once the
precise correspondences between AdS and CFT are perfectly revealed, one will be able to
use well-understood non-gravitational quantum theory to formulate and analyze mysterious
quantum gravity. In other words, the problem of quantum gravity will be automatically
solved. Therefore, working on understanding AdS/CFT better is a crucial key to exploring
quantum gravity.
Despite its great success, there are still many big issues with the current stage of studies on
quantum gravity using AdS/CFT. First, although AdS/CFT is in principle a correspondence
between quantum AdS gravity and CFT, it is examined almost only in the classical limit.
The classical limit is a special case where gravity is effectively described by general relativity.
Second, even at the classical AdS limit, the dictionary that tells us which object in AdS
corresponds to which object in CFT is not completely understood. ...

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