Abstract
We study the scaling dimension \( {\Delta}_{\phi^n} \) of the operator 𝜙n where 𝜙 is the fundamental complex field of the U(1) model at the Wilson-Fisher fixed point in d = 4 − ε. Even for a perturbatively small fixed point coupling λ∗, standard perturbation theory breaks down for sufficiently large λ∗n. Treating λ∗n as fixed for small λ∗ we show that \( {\Delta}_{\phi^n} \) can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in
We explicitly compute the first two orders in the expansion, ∆−1(λ∗n) and ∆0(λ∗n). The result, when expanded at small λ∗n, perfectly agrees with all available diagrammatic com- putations. The asymptotic at large λ∗n reproduces instead the systematic large charge expansion, recently derived in CFT. Comparison with Monte Carlo simulations in d = 3 is compatible with the obvious limitations of taking ε = 1, but encouraging.
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ArXiv ePrint: 1909.01269
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Badel, G., Cuomo, G., Monin, A. et al. The epsilon expansion meets semiclassics. J. High Energ. Phys. 2019, 110 (2019). https://doi.org/10.1007/JHEP11(2019)110
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DOI: https://doi.org/10.1007/JHEP11(2019)110