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

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

Event time:

Tuesday, October 1, 2019 - 4:00pm to 5:00pm

Location:

Sloane Physics Laboratory (SPL), Room 52

217 Prospect Street

New Haven, CT
06511
Event description:

Open to:

undergraduate

Contact:

(see "Description" above)