Non-Perturbative Strings and Field Theory
There have always been many connections between string theory and field theory. A key development in the subject was the realization that gauge theories with large gauge groups could provide a dual description of string theory in a spacetime with certain asymptotic conditions. The gauge theory and string theory describe the same physics: this is a `holographic' duality, meaning that the specification of the interactions in the field theory translate into asymptotic boundary conditions on the spacetime.
The most developed example of such a duality is the AdS/CFT conjecture. AdS refers to anti-de Sitter space, a space of constant negative curvature, while CFT stands for a conformal field theory. The conjecture relates string theory in a spacetime where the non-compact part is asymptotically AdS to a CFT living in a space isomorphic to the boundary of AdS. This conjecture has been extensively tested, applying special properties of the dual field theory to obtain results valid at strong gauge coupling which can be compared to predictions from string theory in the bulk. For instance, Valya Khoze and collaborators showed that the structure of the field theory multi-instanton moduli space agrees with expectations from string theory. In addition the correspondence has been of great use to understand properties of strongly coupled gauge theories using the gravitational description.
This development has opened up new horizons in both string and field theory. The field theory provides a definition of string theory which goes beyond the usual perturbative description, encompassing processes such as black hole formation. Thus, this description is sufficiently powerful to be able to answer interesting questions in quantum gravity. We are interested in further understanding the description of spacetime from the dual field theory point of view. For example, the field theory provides an explanation of the thermodynamic properties of bulk black holes, but it is difficult to understand the meaning and description of the event horizon in the bulk from this perspective; we have made extensive contributions to understanding this. We have also been involved in the construction of smooth bulk geometries which can be identified with pure quantum states in the field theory.
In field theory, the bulk description can be used to perform calculations at strong coupling. This realized earlier suggestions that some dual classical description existed for gauge theory in this regime. The aim is to extract useful lessons about realistic gauge theories from this correspondence. A large variety of examples have been studied. Some of these involve singular geometries in the bulk, and understanding the physical resolution of these singularities plays an important role in extracting information about the gauge theory.
Solitons and states in the CFT
Potential projects in AdS/CFT