String Theory, Gauge Theory and Duality

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The elementary constituents of matter studied in current high-energy physics experiments appear as point-like objects. The interactions among these particles are so far successfully described by a theoretical framework known as quantum field theory, gauge theories being an important example for the formulation of the particle physics Standard Model (SM). At large scales, the behaviour of our Universe is well explained by Einstein's General Relativity, a classical field theory describing gravity in geometrical terms. However, as the Large Hadron Collider (LHC) is entering its discovery phase and the Planck Space Observatory is harvesting high precision data, our current theories will soon face some new stringent tests. It is widely expected that both the SM and General Relativity turn out to describe reality only in an approximate fashion. String theory may be seen as a generalisation of the field theory framework on which the SM is based: in string theory the fundamental constituents are one- or multi-dimensional objects (i.e. strings and branes) that can vibrate. String theory implies some surprising new features with respect to the SM, such as the existence of extra space-dimensions and a new type of symmetry between matter and forces (supersymmetry). Moreover, while at large distances the theory agrees with General Relativity, it predicts interesting novelties also in the description of the gravitational force. Research at Queen Mary aims to expand our knowledge of string and quantum field theories both at the conceptual and the computational level. A surprising feature of string theory is its ability to generate new ideas and techniques that can be employed in different contexts. A recent example of this, which is relevant for the current proposal, is the string inspired relation between a certain type of interaction among gluons (MHV amplitudes) and the geometrical problem of finding the area whose boundary is a particular polygon. Research at QM contributed to the understanding of this relation and is actively studying new and powerful ways to calculate amplitudes without using the traditional approach of Feynman diagrams. Particular attention is devoted to a very special case of the gauge theory, known as N=4 super Yang-Mills. These new techniques are being generalised to handle other interesting quantities beyond the physical amplitudes and are being applied to different quantum field theories. A surprising property of N=4 super Yang-Mills theory is that it has a completely equivalent, dual description in terms of strings and branes propagating on negatively curved geometries. Since Maldacena's discovery of this duality (AdS/CFT), the 'holographic' relation between string and quantum field theories has been thoroughly studied. Research at Queen Mary aims to derive the precise dictionary between the gauge and the string theory formulations of this theory and to understand the mathematical basis of this duality. The dynamics of string and branes is being analysed at QM both from the AdS/CFT perspective and in the more general string/M-theory context. This is leading to new conceptual results about the physical properties of black holes, the duality relations between apparently different theories and the geometrical properties of space-time itself. Advances in the research areas mentioned above are likely to be very relevant in different areas of science. Cosmology is one of the subjects that can benefit from our current research and various applications of string theory to this field are being studied at QM. Particle physics and the analysis of LHC data will benefit from new techniques developed to calculate gluon amplitudes. Theoretical ideas related to the AdS/CFT duality are also being used at QM to analyse interesting condensed matter systems. Finally there is a beneficial flow of ideas between mathematics and string theory in various areas ranging from geometry to group theory.