Unravelling the Non-Perturbative Structure of Gauge Theory

A century ago Max Planck postulated that energy is not a continuous quantity, but rather that it comes in discrete units called quanta. These are so small that we do not normally see their effect in our day-to-day life. Nonetheless they fundamentally alter the properties of a theory. This discretisation of the energy, and other quantities, in a classical theory, is known as quantisation. It has been carried out for electromagnetic interactions, as well as for nuclear forces, known collectively as gauge theories. The predictions made by these quantum gauge theories have been matched with experiments to a spectacular degree of precision.For example, the gauge theory of nuclear forces predicts that protons and neutrons are composed of extremely small particles called quarks, which have since been found experimentally. Quarks are different from other particles such as electrons or protons, in that they do not occur on their own. They interact so strongly with one another that a single quark very quickly attracts other quarks to form observed particles such as protons or neutrons. This property, known as confinement, occurs because of the strong, or non-perturbative, nature of nuclear interactions. At present we have no way of deriving from the gauge theory of nuclear interactions how confinement happens. It is one of the big challenges of theoretical physics today.In an independent development, twenty years after Planck's discovery, Einstein formulated a theory of gravity known as General Relativity (GR), which generalised Newton's law of gravity. In GR spacetime is curved by matter, such as the earth, and it is this curvature that makes objects 'fall' under gravity. GR too has been verified in many experiments. However, GR is a classical theory, with energy being a continuous quantity.Given the success of quantising gauge theories, physicists tried to quantise GR. It turns out that the usual quantisation procedure cannot be applied to GR! But energy is a universal quantity in physics; it cannot be that some parts of the physical world, such as the atom are described by theories in which energy is quantised, while others, describing planets and stars are described by theories in which energy in continuous! The problem of quantising gravity has become one of the central theoretical problems in physics.An alternative way to quantise gravity has been to use string theory. In this approach, fundamental particles of nature (such as electrons, quarks or gravitons) are not particles at all but rather strings. We have not observed these strings to date because they are very small indeed. So far, the acceptance of string theory comes from the theoretical fact that they give a consistent quantum gauge and gravity theory.Recently, the two, apparently very different, problems of quantising gravity and explaining confinement have been related to one another via the gauge/string correspondence. This incredible result, predicted some 30 years ago by 't Hooft and recently presented by Maldacena, shows that a theory of gravity can be described by a theory of nuclear-like interactions! This correspondence is a fascinating bridge between two of the most challenging problems in modern theoretical physics. I believe that this correspondence can teach us a great deal about the nature of confinement in gauge theory on the one hand, and about the quantisation of gravity on the other.In my work I intend to use the gauge/string correspondence to learn about gauge theory phenomena such as confinement. In particular, I intend to find out how a theory of gravity can re-arrange itself into a theory of gauge interactions. In doing this I will be paying particular attention to the 'stringy' nature of the gravitational theory. Initially, my work will focus on gauge theories which are more symmetric than the theory of nuclear interactions. Despite being more symmetric, such theories possess many similarities with those in the real world. Since the procedure I propose for understanding this re-arrangement does not rely explicitly on the extra symmetries present in the gauge theory, already for such theories I expect to learn a great deal about gauge theory behaviour.Once an understanding of this re-arrangement of string theory into a gauge theory is understood for the more symmetric theories, I intend to apply it to gauge theories with less symmetry, in order to learn more about the gauge theory of nuclear interactions. Finding out how the 'stringy' gravity theory re-organises itself into these realistic gauge theories, I believe, will teach us about non-perturbative gauge theory dynamics such as confinement.A century ago Max Planck postulated that energy is not a continuous quantity, but rather that it comes in discrete units called quanta. These are so small that we do not normally see their effect in our day-to-day life. Nonetheless they fundamentally alter the properties of a theory. This discretisation of the energy, and other quantities, in a classical theory, is known as quantisation. It has been carried out for electromagnetic interactions, as well as for nuclear forces, known collectively as gauge theories. The predictions made by these quantum gauge theories have been matched with experiments to a spectacular degree of precision.For example, the gauge theory of nuclear forces predicts that protons and neutrons are composed of extremely small particles called quarks, which have since been found experimentally. Quarks are different from other particles such as electrons or protons, in that they do not occur on their own. They interact so strongly with one another that a single quark very quickly attracts other quarks to form observed particles such as protons or neutrons. This property, known as confinement, occurs because of the strong, or non-perturbative, nature of nuclear interactions. At present we have no way of deriving from the gauge theory of nuclear interactions how confinement happens. It is one of the big challenges of theoretical physics today.In an independent development, twenty years after Planck's discovery, Einstein formulated a theory of gravity known as General Relativity (GR), which generalised Newton's law of gravity. In GR spacetime is curved by matter, such as the earth, and it is this curvature that makes objects 'fall' under gravity. GR too has been verified in many experiments. However, GR is a classical theory, with energy being a continuous quantity.Given the success of quantising gauge theories, physicists tried to quantise GR. It turns out that the usual quantisation procedure cannot be applied to GR! But energy is a universal quantity in physics; it cannot be that some parts of the physical world, such as the atom are described by theories in which energy is quantised, while others, describing planets and stars are described by theories in which energy in continuous! The problem of quantising gravity has become one of the central theoretical problems in physics.An alternative way to quantise gravity has been to use string theory. In this approach, fundamental particles of nature (such as electrons, quarks or gravitons) are not particles at all but rather strings. We have not observed these strings to date because they are very small indeed. So far, the acceptance of string theory comes from the theoretical fact that they give a consistent quantum gauge and gravity theory.Recently, the two, apparently very different, problems of quantising gravity and explaining confinement have been related to one another via the gauge/string correspondence. This incredible result, predicted some 30 years ago by 't Hooft and recently presented by Maldacena, shows that a theory of gravity can be described by a theory of nuclear-like interactions! This correspondence is a fascinating bridge between two of the most