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Résumé |
Conformal field theory (CFT) plays a crucial role in understanding phase
transitions, whether quantum or statistical. CFTs can be studied using
perturbative methods, such as the 4-epsilon expansion and the large N expansion.
In this talk, I will introduce an alternative approach: a fixed-dimensional
perturbation theory that incorporates long-range, non-local interactions. I will
demonstrate that by imposing the conformal Ward Identity, it is possible to
recover the data of local CFTs. By re-summing the perturbative series using long-
range solitons (solutions to the nonlinear equation of motion with fractional
Laplacian), we obtain nice results for the critical exponents.
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