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Although the perturbative description of interactions by the splitting and joining of strings provides a solid calculational framework, it does not provide a satisfactory answer to the question `what is string theory?' One of the lessons of field theory is that the appropriate physical description when the interactions are strong may involve a completely different set of variables than when they are weak. In string theory, recent developments have motivated conjectured dualities which relate the theory (with certain boundary conditions) to a field theory, living in a lower-dimensional space which is distinct from the physical spacetime. This can be re-stated as conjecturing that there is a regime in the field theory where it reproduces the physics of the string theory's perturbative description. Thus, the field theory is the answer to the question `what is string theory'.
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. Local operators in the field theory correspond to changes in the asymptotic boundary conditions in spacetime, and changes of scale in the field theory correspond to motion in the direction orthogonal to the boundary. This relation, if taken seriously, implies that non-local observables in the field theory probe the interior of the spacetime.
The field theory provides a dual description of the whole spacetime, including arbitrary fluctuations in the metric in the interior, so this description encompasses processes such as black hole formation. Thus, this description is sufficiently powerful to be able to answer interesting questions in quantum gravity. The conjecture is motivated by previous developments in string theory which had successfully produced a statistical understanding of the black hole entropy, and one of the main ambitions is to apply this conjecture to deepen our understanding of black holes.
This conjecture also gives a calculationally useful effective description of field theories at strong coupling. It had long been thought that some dual classical description existed for gauge theory in this regime, and it had even been conjectured that it would involve a string theory. The conjectured duality has been used to study the qualitative features of field theory, including studies of confinement and thermodynamic phase transitions. We can also extract quantitative predictions, for certain quantities which are protected by supersymmetry, and the conjecture has been extensively tested by comparing these to non-perturbative information from field theory. An important contribution was made by Valya Khoze and collaborators, who have shown that the structure of the field theory multi-instanton moduli space agrees with expectations from string theory.
If we are to extract useful lessons about realistic gauge theories from this correspondence, it is important to find other examples, and understand more detailed aspects which govern more complicated gauge theories. This will involve studying new configurations of intersecting and wrapped branes, and finding new techniques for deriving the supergravity solutions in which the strings propagate in the dual model describing such branes.
For newly discovered dual geometries, work is needed to uncover the details of the dictionary between strings propagating in the dual geometries and the field theory. This gives new predictions for properties of strongly coupled gauge theory. Conversely, the dual gauge theory gives predictions for string propagation in the new backgrounds. In some cases where the dual field theory is non-conformal, the corresponding supergravity geometries are singular. Many of these singularities have been shown to be resolved in the full string (M--) theory. In addition to allowing us to study the field theory, this mechanism will have important consequences for our understanding of gravity.
One of the strangest features of our current understanding is that there are different field theory descriptions for different boundary conditions. We would expect non-perturbative quantum gravity to have a single unified structure. Thus, a crucial long-term goal is to find some new principle which underlies these descriptions, and gives a more general understanding of quantum gravity.
Work in this area is wide-ranging; there are extensive contacts with non-perturbative field theory, and conformal field theory.