Particle/High Energy Theory Seminar: Gabriel Cuomo (École polytechnique fédérale de Lausanne, Switzerland) “The epsilon expansion meets semiclassics”

The epsilon expansion meets semiclassics
In this talk I will study the scaling dimension ∆n 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 λn. Treating λn as fixed for small λ, I will show that the scaling dimension ∆n 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 λn. I will discuss explicitly the computation of the first two orders in the expansion. The result, when expanded at small λn, perfectly agrees with all available diagrammatic computations. The asymptotic at large λn reproduces the systematic large charge expansion, recently derived in CFT. I will also comment on similar results for the U(1) model in 3 − ε dimensions.
Host: David Poland
david.poland@yale.edu