AdSCFT

AdSCFT, commonly written AdS/CFT, stands for the conjectured holographic duality between gravity in anti-de Sitter space and a conformal field theory on its boundary. Proposed by Juan Maldacena in 1997, the best studied example relates type IIB string theory on AdS5 × S5 to four-dimensional N=4 supersymmetric Yang-Mills theory in the large N limit at strong coupling. In this correspondence, a weakly curved or semiclassical gravity theory in the bulk is equivalent to a strongly coupled gauge theory on the boundary, and vice versa. The duality provides a dictionary that maps bulk fields to boundary operators, bulk spacetime geometry to the renormalization group flow, and bulk partition functions to boundary correlation functions.

Key features include holography: all bulk gravitational degrees of freedom are encoded in a lower-dimensional quantum field theory; the conformal symmetry of the boundary CFT matches the isometries of AdS; and the radial coordinate in AdS is interpreted as an energy scale in the boundary theory.

Extensions include AdS4/CFT3 and AdS3/CFT2 setups, as well as various nonconformal and non-supersymmetric deformations that aim to model finite temperature, confinement, or condensed matter systems. The correspondence has been applied to study quark-gluon plasma, transport coefficients, and strongly correlated systems in condensed matter physics, often in regimes inaccessible by traditional methods.

Limitations and scope: AdSCFT remains a conjecture with proofs in limited cases; its useful regime typically requires large N and strong coupling on the gauge theory side, corresponding to a weakly curved classical gravity description on the AdS side. The extent to which it captures real-world QCD or condensed matter systems is an active research area.