Conformal Field Theory (CFT) is a quantum field theory invariant under conformal transformations, which are angle-preserving transformations that can locally scale distances. CFT is crucial in understanding critical phenomena in statistical mechanics and has profound applications in string theory and the AdS/CFT correspondence, providing insights into quantum gravity and the holographic principle.

Conformal Field Theory

Quantum Field Theory (QFT) is a fundamental framework in theoretical physics that blends quantum mechanics with special relativity to describe how particles and fields interact. It serves as the foundation for understanding particle physics and the Standard Model, providing insights into the behavior of subatomic particles and the forces that govern them.

quantum field theory

conformal transformations

angle-preserving transformations

Local scaling of distances

Critical phenomena refer to the behavior of physical systems undergoing continuous phase transitions, characterized by scale invariance and universality. These phenomena are marked by critical exponents, diverging correlation lengths, and fluctuations that dominate the system's properties near the critical point.

critical phenomena

Statistical mechanics is a branch of physics that uses probability theory to study and predict the behavior of systems with a large number of particles, bridging the microscopic laws of physics with macroscopic observations. It provides the framework for understanding thermodynamic properties and phase transitions by averaging over the possible states of a system rather than tracking individual particles.

statistical mechanics

String theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects known as strings. It aims to reconcile general relativity and quantum mechanics, potentially providing a unified description of all fundamental forces and particles in the universe.

string theory

The AdS/CFT Correspondence, also known as the Maldacena duality, posits a relationship between a type of string theory defined in a higher-dimensional Anti-de Sitter (AdS) space and a Conformal Field Theory (CFT) defined on its boundary. This duality provides a powerful tool for understanding quantum gravity and strongly interacting quantum field theories by translating problems in one theory into more tractable problems in the other.

AdS/CFT correspondence

Quantum Gravity is a theoretical framework that seeks to describe gravity according to the principles of quantum mechanics, aiming to unify general relativity with quantum physics. It remains one of the most significant unsolved problems in theoretical physics, with various approaches like string theory and loop quantum gravity being actively explored.

quantum gravity

The Holographic Principle suggests that all the information contained in a volume of space can be represented as a theory on the boundary of that space, implying that our 3D universe could be a projection from a 2D surface. This principle arises from the study of black hole thermodynamics and quantum gravity, offering profound implications for understanding the nature of space and time.

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