The epsilon expansion meets semiclassics

Abstract: In this talk, I will study the scaling dimension of the lightest operator of charge n in the U(1) model at the Wilson-Fisher fixed point in 4-ε dimensions. Even for a perturbatively small fixed point coupling λ, standard perturbation theory breaks down for sufficiently large λ n. Treating λ n as fixed for small λ, I will show that the scaling dimension can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in a series in the coupling whose coefficients are fixed functions of λ n. I will discuss explicitly the computation of the first two orders in the expansion. The result, when expanded at small λ n, perfectly agrees with all available diagrammatic computations. The asymptotic at large λ n reproduces the systematic large charge expansion, recently derived in CFT. Similar results can be derived in the U(1) model in 3-ε dimensions. I will briefly comment on the application of similar ideas in the calculation of other observables, such as three-point functions of charged operators. This talk is based on arxiv.org/abs/1909.01269 and arxiv.org/abs/1911.08505.

other condensed mattersoft condensed matterstatistical mechanicsstrongly correlated electronssuperconductivitygeneral relativity and quantum cosmologyHEP - theorymathematical physicschaotic dynamicsfluid dynamicsquantum physics

Audience: researchers in the topic

Kadanoff seminars