The common aim of scientists has always been to explain natural phenomena by means of mathematical equations. Natural phenomena cover everything you can see around, and many things you don't see! from the origin of the universe and black holes to the atom and even more fundamental particles.
My field is theoretical physics and more precisely string theory, which is an attempt at a comprehensive and unified explanation for every kind of force and every phenomenon that exists in nature. Science is usually not about answering questions, but rather about asking the right questions. In this case, the right question is: what is the form of the electron and other sub-atomic particles? the answer that string theory gives is that particles are not zero-dimensional ‘points’ (like the image of an electron you might have acquired from your science text books) but rather one-dimensional string-like structures. If string theorists are right, the whole space, and everything in it, is made up of these tiny sub-atomic ‘strings’.
The very simple assumption that fundamental particles are tiny strings has fascinating consequences. First, these strings can only exist in 10 space-time dimensions! in addition to the four with which we are familiar – height, width, depth and time - string theory says that there are other six dimensions, which are so small/compacted, that we can't access them yet (but we may in the near future!). The second, and maybe more striking, consequence is that string theory should explain, with a single equation, every phenomenon of nature!
Since string theory is, in essence, a single, unified theory, if it offers an accurate description of the universe as a whole, it should be possible to demonstrate that it is compatible with a number of other ways of understanding and interpreting particular phenomena. Specifically, we need to show that it is consistent both with the theory of gravity ( that governs the behaviour of big things like planets) and quantum mechanics or 'gauge theories' (that govern the behaviour of atoms and sub-atomic particles). Conversely, if string theory is true, it should be possible to find a way to describe in a unified manner both, the theory of gravity and quantum mechanics/gauge theories.
Inevitably, this has proved very challenging, but there are a number of areas in which it has been possible to establish a ‘duality’ between a form of gauge theory and a theory of gravity. This means that it can be shown that the particular gauge theory can also be expressed in terms of the seemingly unrelated theory of gravity, and vice versa. And the more such dualities can be established, the more convincing the claims for string theory become – and that’s where I come in. The first precise duality was proposed by Juan Maldacena, in 1997, and since then about 8000 papers have slowly built the dictionary of equivalence between these different kinds of theory. Part of my research involves adding new entries to this dictionary.
Another direction I have been involved in, concerns a different class of dualities, between a type of gauge theory called a super-symmetric gauge theory (one that describe what happens in four dimensions), and a set of theories called conformal field theories (that describe what happens in two dimensions). My duality is known as the AGT (Alday-Gaiotto-Tachikawa) Conjecture and has become linked several areas of physics and mathematics.