One of the greatest unsolved problems in physics is the unification of quantum mechanics and general relativity. Gravitation is described by general relativity, whereas quantum mechanics describes the behavior of matter at the microscopic level and other known interactions in nature, including electromagnetism. String theory has been used to bridge the gap between these two theories, since it provides a consistent theory of quantum gravity. In string theory, all fundamental particles are tiny strings vibrating in spacetime. A remarkable feature of string theory is holography, which states that when you have a string theory in a given volume, it can be completely reconstructed using only the information on the boundary of that volume. Holography occurs in gravitational theories, and as such, we will develop new techniques to understand it and quantum gravity by analytically calculating all the interactions of some string theories and filed theories on the boundary, such as N=4 Super-Yang-Mills.

What is quantum gravity? This fundamental question is still up in the air, despite decades of research and progress in the field. Quantum mechanics is used to understand microscopic phenomena, and a quantum theory of gravity is essential for understanding the origin of the universe and black holes. While the other known interactions have well-established quantum descriptions, gravity remains a mystery.

These questions have intrigued me since my student days. In my doctorate, I studied string theory, a consistent theory of quantum gravity. String theory posits that the fundamental particles are small vibrating strings rather than points. The theory is complex and has many open problems, but the attempt of this project is to systematically understand the holographic phenomenon, which describes physics in a volume by studying the boundary of space.