Some of the research areas studied by the group are outlined below. Detailed descriptions of the research interests of individual group members may be found on their webpages.
String theory and Calabi-Yau manifolds
Prof Philip Candelas, FRS, Prof Xenia de la Ossa
Calabi-Yau manifolds may be used to realize four-dimensional particle physics models via string theory constructions. The study of Calabi-Yau compactifications leads to interesting relationships between conformal field theory, differential geometry and algebraic geometry. The group's work has recently focused on compactifications of heterotic string theory and F-theory, Calabi-Yau manifolds with small Hodge numbers, and topological transitions between Calabi-Yau threefolds. We have also been exploring connections to number theory via the arithmetic of Calabi-Yau manifolds.
Prof Joseph Conlon, Prof Andre Lukas
Several members of the group study phenomenological applications of string theory i.e. developing string theory realizations of Standard Model and Beyond-the-Standard-Model physics. This includes Standard Model constructions of string theory through compactification on Calabi-Yau manifolds with appropriate gauge bundle backgrounds. These can be automated using powerful techniques from algebraic geometry with an ability to perform computer scans over many possible models. It also involves the study of moduli stabilization and mechanisms of supersymmetry breaking in string theory. Such studies are carried out both from the perspective of the low energy supergravity theory and also directly on the string worldsheet. We also study string theory applications in cosmology, for example the construction of inflationary potentials in string theory.
Twistor theory and twistor strings
Prof Lionel Mason
Twistor theory is a programme originally introduced by Roger Penrose as an approach to the unification of quantum theory and general relativity. Twistor theory now finds wide application to problems in mathematical physics, geometry, nonlinear differential equations, and particularly integrable systems. More recently the group's work has focused on twistor strings and twistor approaches to scattering amplitudes.
Conformal field theory and quantum gravity
Prof John Wheater
Conformal symmetries and their extensions are a powerful tool in the study of field theories. Logarithmic conformal field theories have been a major activity for many years; at present we are working on the properties of these theories in the presence of boundaries. This is of relevance to systems as diverse as a recoiling D-brane and densely packed polymers. Quantum gravity is studied in two dimensions, where it has many equivalent descriptions including as a conformal field theory, and in higher dimensions where conformal structures are used in understanding the foundations of the subject.
Gauge-string duality, holography, AdS/CFT correspondence
Prof Luis-Fernando Alday, Prof James Sparks, Prof Andrei Starinets
Gauge-string duality, or the AdS/CFT correspondence, is a conjectured duality between strongly coupled quantum systems and classical gravity in higher-dimensional spacetimes. This is a wide-ranging and actively studied area of theoretical physics, and the group's work covers a number of different aspects and applications. Our research covers such areas as: applications to strongly coupled supersymmetric gauge theories in diverse dimensions; scattering amplitudes in Yang-Mills theory; aspects of AdS/CFT in supergravity and geometry; applications to strongly coupled plasmas, relating transport properties (viscosity, thermal conductivity, diffusion constants) to excitation spectra of black holes.