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String Theory and Mathematical PhysicsString theory is an interdisciplinary field of fundamental research, with very fruitful interfaces to high energy physics, general relativity, cosmology, statistical physics and mathematics. It currently addresses two distinct and fundamental problems of modern theoretical physics: The unification of all interactions, including gravity, and the physics of strongly interacting quantum field theories. String Theory and GravityString theory is a far reaching generalization of quantum field theory. It is based on the premise that the fundamental constituents of Nature are strings, that is, one-dimensional rather than point-like objects. Elementary particles such as the electron, photon and also the graviton arise as particular vibrational modes of the string. By allowing strings to split and join, one recovers all known fundamental forces, including gravity. On sufficiently large scales, much larger than the size of the string, the stringy version of gravity looks like Einstein's theory of general relativity. The extended nature of strings, however, leads to important deviations from general relativity at small scales. Thereby, string theory succeeds in consistently combining gravity with the principles of quantum physics. Indeed, some important examples show that the stringy version of quantum space-time is somewhat fuzzy or, in more scientific terms, that the quantum theory of strings can be regular even in cases when the space-time background is singular. When applied to cosmological evolution, big-bang singularities or black-hole physics, this smoothing effect of string theory might be able to resolve the conceptual problems that have been raised in the endeavor to understand quantum effects of the gravitational field. String Theory and Gauge TheoryGauge theories have been used for several decades to model Nature. In perturbation theory, many interesting quantities can be computed, leading to theoretical predictions of stunning accuracy. Perturbative gauge theory, however, is restricted to a régime in which the couplings between particles can be considered small. This is not always the case. Strongly coupled gauge physics for example is responsible for the observed confinement of quarks. More recently, a strongly coupled quark-gluon plasma has been produced in heavy ion collisions at RHIC. According to a seminal proposal by Juan Maldacena, strongly coupled 4-dimensional (super-symmetric) gauge theories may be described through closed strings in a carefully chosen 5-dimensional background. In fact, equivalences - or dualities in the modern parlance - between gauge and string theories emerge, provided the strings propagate in a 5-dimensional space of constant negative curvature. Such a geometry is called an Anti-deSitter (AdS) space and the duality involving strings in an AdS background became known as the AdS/CFT correspondence. Through this duality, string theory techniques are beginning to give access to strongly coupled gauge physics. The string theory group at DESY pursues research on a variety of issues, ranging from string theory in Anti-deSitter spaces, through aspects of quantum (stringy) geometry, to problems in 2-dimensional field theories and statistical physics. It profits from a very stimulating research environment at DESY and Hamburg University. This includes groups working in string phenomenology, astroparticle physics, quantum chromodynamics, mathematics and mathematical physics. The interaction is supported by the German Science Foundation (DFG) through a Collaborative Research Center Sonderforschungsbereich 676 on Particles, Strings and the Early Universe. DESY's string theory group is also part of Hamburg's Center for Mathematical Physics, a common initiative with Hamburg University. Finally, the string theory group also hosts an Excellence team on Non-linear Sigma models in String Theory that is funded by the European Union. Some suggested lecture notes for further reading:
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