Gauge/string dualities relate gauge theories (theories without gravity) to string theories (theories of gravity), in such a way that the gravity theory emerges holographically from the gauge theory. In addition, they relate strongly to weakly coupled theory and thus yield powerful methods in analysing theories beyond perturbation theory.
A powerful tool in the study of string theory is known as string theory/gauge theory dualities. These dualities can address certain questions in gauge theory that are out of reach of perturbative field theory. The basic idea is that string theory in d+1 space-time dimensions arises holographically from gauge theory in d dimensions, just like a two-dimensional hologram can appear to have a third-dimension when correctly illuminated.
The original example of such a duality, first proposed by Maldacena in 1997, is known as anti-de Sitter space/conformal field theory duality (AdS/CFT duality). In its original formulation this duality states the full (quantum) equivalence of type IIB superstring theory on a five-dimensional anti-de Sitter space, a space of constant negative curvature, and maximally supersymmetric Yang—Mills theory on its four-dimensional conformal boundary. As such, it relates a theory with gravity (the string theory) to a theory without gravity (the Yang—Mills theory).
The AdS/CFT duality has been generalised to various other settings and has found many applications.
Recent important developments that use these ideas include the construction of gauge theory scattering amplitudes and attempts of providing microscopic descriptions of phenomena in condensed matter physics and fluid dynamics (gravity/fluid correspondence). Still we do not know yet why and how this duality can work. For instance, we do not know how the geometry and the local excitations on the gravity side are encoded in the dual non-gravitational theory. Part of our research involves trying to understand these issues.