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Quantum Field Theory and Applications

Sofian Teber

Systems composed of a large number of interacting particles are subject to fascinating emergent phenomena such as phase transitions. Of current interest are the so-called interacting (planar) Dirac systems that are condensed matter physics systems characterized by gapless bands, strong and long-ranged electronic/elastic interactions and emergent Lorentz invariance deep in the infra-red. The corresponding effective models correspond to (gauge) field theories that are generally not exactly solvable. In order to be appreciated, the properties of such systems require studies that go beyond common mean field approximations or even basic leading order calculations, especially in regimes of strong correlations. Quantum (and statistical) field theory (QFT) offers a remarkable universal framework to address such issues in an analytical way and may even serve as a benchmark for non-perturbative approaches (such as the functional renormalization group).

With an expertise in QFT computations that can rapidly reach a formidable level of complexity, the group has contributed to analytically elucidate the phase structure of a number of models such as conformal three-dimensional QED (QED_3) that is a well-known effective field theory describing a variety of Dirac-like systems such as high-Tc superconductors, planar antiferromagnets and graphene. Some significant achievements include :

-  Dynamical mass generation in spinor QED_3 (with A. Kotikov);

-  Fate of infra-red singularities in quenched spinor QED_3 (with V. Gusynin, A. Kotikov and A. Pikelner);

-  The Landau-Khalatnikov-Fradkin transformation and zeta-structure of spinor QED_4 (with A. Kotikov);

-  Renormalization group flows in flat polymerized membranes (with S. Metayer, O. Coquand and D. Mouhanna);

-  Critical exponents and phase structure of supersymmetric QED_3 and pure scalar QED_3 (with S. Metayer).