The Geometry of Supergravity Solutions and Applications

The two really big theories in theoretical physics are quantum theory and our theory of gravity, Einstein's theory of General Relativity.Quantum theory describes the physics of the really small: atoms, electrons, protons and all of the particles observed when these particles are smashed into each other at very high energies in particle accelerators. The quantum world is very weird as it says that sometimes particles actually behave like waves and vice-versa. But the weirdness is really there: the quantum theory of particle physics has been tested to incredible precision. We know that there are three quantum forces: the electromagnetic, the weak and the strong nuclear force. This magnificent edifice is sometimes called the Standard Model of particle physics.Gravity, on the other hand hand, is quite different. General Relativity says that the phenomenon of, say, an apple falling onto Isaac Newton's head, is a manifestation of the curvature of space-time. To get a flavour of this, imagine a big latex rubber sheet with a shot-put sitting in the middle stretching it down. If we now put a marble on the sheet, it will roll toward the shot-put as if it is being pulled by some force.General Relativity is also very accurate, having been tested in many different ways. One of the most interesting aspects of the theory is that it predicts the existence of black holes. In a black hole gravity is so strong, that is, the curvature of spacetime is so great, that even light cannot escape. We now think that all galaxies have a huge black sitting at their centre. General Relativity is also the basis for our theory of the origin of the universe, that everything began about 10 billion years ago in a very tiny compressed state and then exploded - the Big Bang .So, two beautiful theories, the Standard Model and General Relativity, and both very accurate. But...they are mathematically incompatible! How can this possibly be? The point is that the two theories are associated with very different scales: on small scales, for current particle physics, gravity is so weak that we can just forget about it. Similarly, General Relativity is applicable on very large scales when all other particle forces are negligible. This is why we can have the two incompatible theories happily co-existing.However, we know that there are some situations when we need both theories: for example inside black holes and at the Big Bang. A theory that unifies the two is called a theory of quantum gravity. We work on a candidate quantum gravity called string theory. The main idea of string theory is that everything is really made up of very, very tiny little loops or segments of string. The oscillations of these strings, like the different notes on a guitar, would each become, via the quantum weirdness, a different elementary particle. If it oscillates one way it's an electron, if it oscillates another way it's a proton and so on. Understanding the mathematics of exactly how this might happen is something that we are working on.Symmetry has been a major guiding principle in constructing the Standard Model and General Relativity. Now, every particle that we know of is either a boson or a fermion. The bosons, a photon for example, are associated with forces, while the fermions, an electron for example, are associated with matter. A very interesting symmetry, called supersymmetry, is essentially the unique way to connect bosons with fermions, or equivalently forces with matter. It is a central component of string and, based on a lot of hints, we think obtaining a deeper mathematical understanding of supersymmetry in string theory will lead to a deeper understanding of string theory itself. This is what we are proposing to work on and we hope that it will provide a significant step on the journey to determine whether or not Nature is described by string theory.