Status  Confirmed 
Seminar Series  COURS 
Subjects  hepth 
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 WilsonFisher 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 nontrivial 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 threepoint functions of charged operators. 
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