I can provide you with some information about the three theories you mentioned: string theory, loop quantum gravity, and quantum holonomy.
String Theory: String theory is a theoretical framework that attempts to unify gravity with the other fundamental forces of nature, such as electromagnetism and the strong and weak nuclear forces. It suggests that the fundamental building blocks of the universe are tiny, vibrating strings. String theory is a mathematically rich and complex theory that has connections to various areas of physics, such as particle physics and cosmology. It has been a subject of extensive research and has led to many interesting mathematical and conceptual developments.
Loop Quantum Gravity: Loop quantum gravity is a quantum theory of gravity that seeks to describe the gravitational field at the fundamental level. It proposes that space itself is quantized, meaning that space is made up of discrete units or "atoms" of space. Loop quantum gravity introduces the idea of "spin networks" to describe the structure of space, and it employs techniques from quantum mechanics to study the quantum properties of space and time. Loop quantum gravity is an active area of research, aiming to provide a quantum description of gravity compatible with the principles of quantum mechanics.
Quantum Holonomy: Quantum holonomy refers to the application of quantum theory to the concept of holonomy, which is a geometric property associated with the parallel transport of vectors in curved space. Quantum holonomy studies the quantum effects that arise when considering the evolution of quantum states under parallel transport around closed loops in a curved space. It has connections to areas such as quantum field theory and quantum gravity.
The choice of which theory to study depends on your specific interests, background, and career goals. Each theory offers unique insights and challenges, and they are all active areas of research. It may be helpful to explore the foundational principles, research progress, and open questions associated with each theory to determine which one resonates with your interests and objectives.