Non-perturbative Phenomena and Background (In)dependence in Field and String Theory

• Applicant: Professor Dr. Murad Alim
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2010 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 184125276

Field theories describe a broad range of physical phenomena. Many field theories exhibit dualities which exchange strong and weak coupling together with an exchange of fundamental and non-perturbative degrees of freedom. Understanding dualities has led to a great leap forward for both field and string theories which furthermore incorporate the coupling to gravity. Within string theory, a geometrical meaning can be given to dual formulations of the same theory. Furthermore it is possible to scrutinize the dependence of the theory on its couplings and parameters, i.e. its background dependence. The gained insights allow exact computations of physical quantities. Moreover addressing the question of background dependence has led to intriguing new insights allowing to connect and rethink some of the most fundamental physical notions. The goal of this research program is to extend and deepen the understanding of background dependence of string theories and the possibility to give a background independent meaning to physical quantities. The focus hereby is on phenomena which are related to the perturbative loop expansion of string theory which is governed by the string coupling constant. Non-perturbative effects with respect to this coupling are the D-branes, which are the boundary conditions of string theory. This expansion moreover corresponds to coupling field theories to gravity. Prospects of this research for four-dimensional physical theories are to obtain a precise handle on the effective couplings of physical theories engineered by D-brane setups and to obtain insights into an effective theory of quantum gravity. Furthermore, insights into the non-perturbative completion and S-duality of string theory are expected. On the mathematical side these very concepts are subject of research in the field of mirror symmetry where physical dualities are translated into surprising relations of different areas in mathematics and allow to compute mathematical invariants.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Cumrun Vafa