The thermodynamics of a black hole
3.2
Holographic universe
Juan Maldacena first published a paper in 1997 regarding AdS/CFT (anti-de-Sitter/conformal-field- theory ) duality (Maldacena, 1997). With the work of t’Hooft and Susskind, this eventually developed
into a conjecture of the holographic universe which led to the solution of the information paradox. Throughout the rest of the dissertation, the following terms: AdS/CFT duality, gauge-gravity correspondence, holographic universe and holographic principle will be used interchangeably as they all refer to the same theory. The duality (Nicolaides, 2021) links the interior (AdS) with the boundary (CFT). To visualize this relationship, imagine a cube. A cube is a 3-dimensional object, and the boundary of that cube are the square faces which are 2 dimensional, which is 1 dimension lower than the cube. The interior is simply everything inside the boundary, and 3-dimensional. Thus, we notice that the interior has 1 more dimension than the boundary. While the analogy of the cube is 3-dimensional with a 2-dimensional boundary, a holographic universe would be 5-dimensional with a 4-
dimensional boundary. It is this difference that creates confusion, as higher dimensions are incredibly difficult to comprehend. Therefore, a cylindrical analogy that is not entirely true but easy to visualize can be used, illustrated here.
In a holographic universe, our reality would be a 5-dimensional AdS space-time (thinking back to the analogy, the inside of the cube). The boundary/edge is a 4-dimensional conformal non-gravitational space-time. Information stored on that 4-dimensional boundary is projected into this interior, resulting in our reality. Looking back at the holographic principle, this is very similar to information in a black hole (Caltech, 2020). In black hole complimentary theory, information is stored on the surface of the event horizon and is also stored inside the black hole, thus inside the black hole is a projection of information. This is very similar to a holographic universe, apart from the different number of dimensions. Due to the complexity of the theory, it is essential that the interior AdS region has negative curvature, thus it is named anti-de-Sitter. This relationship between the 4-dimensional boundary and 5-dimensional interior is explained by AdS/CFT duality. The interior of the universe and the boundary of the universe seem completely different and possess different laws but somehow these two things are equivalent. Hence information is first stored on the boundary, but then projected onto the interior. A good example to examine is a tree. Its size, colour, mass, shape, and position are all information stored on the boundary, and this information is then projected into the interior, and we interpret this as a tree (Backreaction, 2021). Maldecana’s conjecture and this idea can be summed up very elegantly by the following: ‘ String theory on AdS × S5 ~ gauge theory on the 4D border - where ~ is the symbol of the duality ’ (Luminet, 2016).
Thus, gauge theory is the specific type of conformal field theory in this situation and string theory describes the interior of the universe. AdS/CFT duality is often referred to as gauge/gravity correspondence, gauge referring to the boundary and gravity referring to the interior.
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