Edouard Brezin
Ecole Normale Superieure
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Primary Section: 13, Physics Membership Type:
International Member
(elected 2003)
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Research Interests
I have used quantum field theory, mainly for applications in statistical physics. I have used the field-theoretic formulation of the renormalization group for critical phenomena (equation of states, corrections to scaling, etc) . I have shown that the low temperature phase, in the case of continuous symmetry breaking, is described by a non-linear sigma model, leading to an expansion of critical exponents in powers of the dimension of space minus two. I have shown that the instanton method may be used to characterize the large order behavior of pertubation theory, which in turn allows one to make precise theoretical estimates. I have applied field theory techniques to condensed matter problems such as the theory of critical wetting, or the study of phase transition from a normal metal to a type II superconductor under a magnetic field. I have been interested in field theories with a large number of colors. This has led to a representation of two-dimensional quantum gravity, random fluctuating surfaces, i.e. bosonic closed string theories, in terms of random matrices. We have shown that the scaling limit of such models is related to integrable hierarchies such as KdV flows. I have worked on the basis for the universality of the correlations of eigenvalues in the local limit for random matrices.
