Status Confirmed Seminar Series COURS Subjects hep-th Date Tuesday 3 December 2019 Time 11:30 Institute LPTENS Seminar Room LPT Library Speaker's Last Name Cuomo Speaker's First Name Gabriel Francisco Speaker's Email Address Speaker's Institution Title 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 $4-\varepsilon$ dimensions. Even for a perturbatively small fixed point coupling $\lambda$, standard perturbation theory breaks down for sufficiently large $\lambda n$. Treating $\lambda n$ as fixed for small $\lambda$, 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 $\lambda n$. I will discuss explicitly the computation of the first two orders in the expansion. The result, when expanded at small $\lambda n$, perfectly agrees with all available diagrammatic computations. The asymptotic at large $\lambda n$ reproduces the systematic large charge expansion, recently derived in CFT. Similar results can be derived in the $U(1)$ model in $3-\varepsilon$ 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. arXiv Preprint Number Comments Attachments

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