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arXiv · 1911.08505

Feynman diagrams and the large charge expansion in $3-\varepsilon$ dimensions

Gil Badel·Gabriel Cuomo·Alexander Monin·Riccardo Rattazzi
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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 $d=4-\varepsilon$ can be computed semiclassically for arbitrary values of $\lambda n$, where $\lambda$ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the $U(1)$ model in $3-\varepsilon$ 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 $O(n^0)$ contribution to the scaling dimension of large charge operators in $3d$ CFTs.

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Gil Badel, Gabriel Cuomo, Alexander Monin, Riccardo Rattazzi. 2019-11-19. Feynman diagrams and the large charge expansion in $3-\varepsilon$ dimensions. https://doi.org/10.1016/j.physletb.2020.135202

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