The classic reason for working on string theory is to solve the problem of quantum gravity. Physicists aim to obtain a consistent quantum theory of gravitational interactions, and then to understand in detail how it works. This motivation still drives research today.
Everyday work involves examining the stringy version of general relativity. Research topics are typically theoretical: they may have limited or no real world application. But thought experiments allow string theorists to better appreciate important properties of their quantum gravity model.
There are two fundamental issues that drive interest in quantum gravity. First physicists want to explain highly curved areas of spacetime, like the centre of a black hole. Secondly we’d like to dispatch the pesky infinities plaguing small-scale gravity. String research has made promising progress on both of these fronts.
General relativity says that spacetime is curved, and Einstein’s equations tell us how gravity warps this fabric. Sometimes spacetime can become infinitely bent, forming a point called a singularity. In this situation the equations break down so we can’t fathom the physics!
A particular example is that of orbifold singularities: it turns out that the equations of string theory continue to work nicely at such singularities. This means we can fully comprehend the physics. Hence strings enable us to move beyond general relativity.
Conifold singularities are another type, more complicated than orbifolds. At a conifold singularity the basic equations of string theory fail. But all is not lost! By including D-branes, physicists can make the theory consistent again. This famous result allows for smooth changes of spacetime.
For cosmological singularities, which may have occurred at the Big Bang, little progress has been made. Despite various attempts, it is not currently possible to solve the equations of string theory in this regime. Currently some researchers are trying to make sense of these singularities.
General relativity generates infinities at short distances, which a quantum theory of gravity should resolve. String theory gives an intuitive picture for the disappearance of infinities, which is supported by detailed calculations. In this picture, the infinities arise because we assume that particles are points. If these points are smeared out to extended strings then the infinite answers disappear for distances smaller than the smearing scale.
This interpretation is a good physical argument, but it is mathematically imprecise. Thankfully it has been confirmed by exact calculations in string perturbation theory. This lends great credence to string theory as a description of quantum gravity.