DescriptionGeneral Relativity and Quantum Mechanics form the two pillars of theoretical physics developed in the early part of the 20th century. General relativity is a classical theory of gravity, which identifies gravity with curvature of spacetime. Quantum mechanics, on the other hand, describes the other forces and fundamental particles. Relativistic quantum theories of fundamental particles are called quantum field theories. Whereas the effects of general relativity are most pronounced in strongly gravitational settings, such as in the context of black holes and cosmology, quantum mechanics exhibits most striking effects on small scales. Within their respective regimes of applicability, these theories have been extensively tested and found to describe the observed universe with remarkable accuracy.The unification of these two theories into a self-consistent and complete theory has been a central goal of theoretical physics for many years. The most successful approach to formulating a fully consistent theory of quantum gravity is String Theory, which is explicitly quantum mechanical while containing gravity; in fact, it unifies all the known forces and particles in nature. It produces surprising new relations between quantum field theories and spacetime. Moreover, it exhibits very interesting mathematical structures and has led to deep mathematical results. We will study the quantum aspects of gravity in string theory. An important part of the project will be exploring the connections to quantum field theory, and how this changes our classical picture of spacetime. It will therefore also involve some study of quantum field theory. The perturbative description of string theory is in terms of a quantum field theory defined on the string, and this already changes our picture of spacetime, through effects such as T-duality. At a deeper level, we have a non-perturbative formulation of string theory through what is called the AdS/CFT correspondence. In this formulation, spacetime is an emergent concept. The fundamental theory is a field theory living in an auxiliary space, and spacetime arises as an approximate effective description of this theory in a classical limit. The spacetime has more dimensions than the fundamental description, so this is referred to as a holographic correspondence. This correspondence casts new light on many questions about spacetime, such as singularity resolution and black hole thermodynamics. This is a rich subject, and there are a wide variety of possible avenues for exploration. The project offers the chance to encounter ideas at the leading edge of an important field of current research. It is also a challenging topic, and will require hard work to master. Prerequisite:Quantum MechanicsCorequisite:General RelativityResourcesThere are large numbers of papers on the web on the subjects of quantum field theory and string theory. A good popular level book which introduces many of the concepts in string theory (and to some extent also talks about quantum field theory) isBrian Greene, ``The Elegant Univers'', Vintage (2000) A very good textbook discussing string theory which should be accessible with knowledge of Quantum Mechanics is Barton Zweibach, ``A First Course in String Theory'', Cambridge University Press, (2004). At a more advanced level, a useful set of lecture notes by David Tong are available online: Lectures on String Theory. There are plenty of other resources on the web, see for example: • Wikipedia • Sunil Mukhi's article on string theory. |
email: Simon Ross