Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines hep-th
Date Mardi 3 Décembre 2019
Heure 11:30
Institut LPTENS
Salle LPT Library
Nom de l'orateur Cuomo
Prenom de l'orateur Gabriel Francisco
Addresse email de l'orateur
Institution de l'orateur
Titre The epsilon expansion meets semiclassics
Résumé 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.
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