Quantum field theories (QFTs) are the language in which the Standard Model is written. They each contain a coupling constant that determines the strength of interactions between particles. When it is small (weak coupling) the theory is easy to solve, in principle. Typically physicists use perturbation theory to obtain good approximate answers.
But when the coupling constant is large (strong coupling), solutions are much more difficult to come by. Our standard perturbative techniques fail in this regime. Understanding the strong coupling behaviour of QFTs is a longstanding problem.
The strong force is strongly coupled at long distances. This means that the further apart two particles are, the more they are attracted to each other by the strong force (see picture left).
At long distances the normal QFT approach doesn’t work, making calculations extremely difficult. This impasse motivates our interest in strongly coupled systems. How can we do the calculations? And what properties will the resulting theory have?
A popular research branch involves using our string toolbox to investigate strong coupling. Dualities play an important role. Suppose you establish a relationship between a strongly coupled field theory A and some weakly coupled theory B. Then you can perform hard calculations in A via easy calculations in B. Dualities employed for this purpose include mirror symmetry, S-duality and the AdS/CFT correspondence.
String theorists studying strong coupling also wield a concept called integrability. Roughly speaking, this allows them to solve problems just by considering symmetries, avoiding any tricky calculations. Luckily symmetry is abundant in fundamental physics: particles can look the same when reflected in a mirror, or spun round like a top. Special cases that can be cracked by integrability are often used to test how well dualities work.
There are probably more people working in the area of strongly coupled field theories than any other in the subject, although many would consider themselves to be field theorists borrowing string ideas. Their research includes both theoretical aspects - integrability is closely related to certain topics in mathematics – and applications to more real world physics.
Currently some researchers are building models of the strong force in real-world situations by taking advantage of dualities. A promising avenue is the study of large nuclei collisions, where long distance strong interactions are crucial to the observed dynamics. Such ideas are not experimental evidence for string theory as the theory of quantum gravity, but are experimental applications of the subject.