Abstract
In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U(1) model at the Wilson-Fisher fixed point in D=4−ε can be computed semiclassically for arbitrary values of λn, where λ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the U(1) model in 3−ε dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal O(n0) contribution to the scaling dimension of large charge operators in 3D CFTs.
Highlights
It is known that, even in a weakly coupled Quantum Field Theory (QFT), there exist situations where the ordinary Feynman diagram expansion fails
In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U (1) model at the Wilson-Fisher fixed point in D = 4 − ε can be computed semiclassically for arbitrary values of λn, where λ is the perturbatively small fixed point coupling
We generalize this result to the fixed point of the U (1) model in 3 − ε dimensions
Summary
Even in a weakly coupled Quantum Field Theory (QFT), there exist situations where the ordinary Feynman diagram expansion fails. Directly in the full theory, bypassing the EFT construction, or, deriving it This was recently illustrated in [13], by focusing on the two-point function of the charge n operator φn in the U (1) invariant Wilson-Fisher fixed point in 4 − ε dimensions. With c’s and d’s having specific calculable values This result nicely matches the universal predictions of the large charge EFT. Eq.s (1) and (2) were verified at large N for monopole operators [16]; the results of Monte-Carlo simulations for the O(2) model at criticality are consistent with the expansion (1) [17], though their present precision is not sufficient to check the universal prediction for d0. Our paper provides an alternative verification where the large charge regime is continuously connected, as λn is varied, to diagrammatic perturbation theory
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