The AdS/CFT correspondence, also known as the gauge/gravity duality or holographic duality, is a profound theoretical idea that establishes a relationship between two seemingly distinct areas of physics: Anti-de Sitter space (AdS) and conformal field theory (CFT). It was first proposed by Juan Maldacena in 1997.
In simple terms, the AdS/CFT correspondence states that certain theories of gravity in higher-dimensional Anti-de Sitter spacetime can be mathematically equivalent to certain conformal field theories living on the boundary of that spacetime. In other words, it suggests that a gravitational theory in one space dimension can be precisely described by a quantum field theory without gravity in one fewer dimension.
This correspondence is significant because it provides a powerful tool to study strongly interacting systems, particularly in contexts where conventional theoretical methods are difficult to apply. One such area where the AdS/CFT correspondence has found numerous applications is condensed matter physics. Here are a few examples:
Strongly correlated systems: Condensed matter systems with strong interactions, such as high-temperature superconductors or systems near a quantum phase transition, are challenging to understand using traditional techniques. The AdS/CFT correspondence offers a new perspective by mapping these strongly correlated systems to classical gravity theories, which can be more amenable to analysis.
Quantum phase transitions: The AdS/CFT correspondence has been employed to study quantum phase transitions, where a condensed matter system undergoes a rapid change in its ground state due to a parameter variation. The holographic approach provides insights into the dynamics of phase transitions and the emergent behavior of quantum critical systems.
Transport properties: The AdS/CFT correspondence has been used to investigate transport phenomena in strongly coupled systems, such as the behavior of electrical conductivity or viscosity. By mapping these transport properties to gravitational phenomena in AdS, researchers have gained valuable insights into the behavior of real-world condensed matter systems.
Entanglement and quantum information: Entanglement plays a crucial role in quantum information theory. The AdS/CFT correspondence has shed light on the connection between entanglement and geometry, offering new perspectives on quantum entanglement entropy and the structure of entangled states in strongly correlated systems.
These are just a few examples of the broad range of applications of the AdS/CFT correspondence in condensed matter physics. The holographic approach has opened up new avenues for studying complex quantum systems, bridging the gap between quantum field theory and gravitational physics.