The large charge limit of scalar field theories, and the Wilson-Fisher fixed point at \(\varepsilon = 0\)

DOI10.1007/JHEP10(2019)201zbMATH Open1427.81112arXiv1908.11347MaRDI QIDQ2283494

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Publication date: 2 January 2020

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Abstract: We study the sector of large charge operators $ph{i}^n$ ($phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-epsilon$ dimensions that emerges when the coupling takes the critical value $gsimepsilon$. We show that, in the limit $go0$, when the theory naively approaches the gaussian fixed point, the sector of operators with $noinfty$ at fixed $g,n^{2}equivlambda$ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator $ph{i}^n$ by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional $O(2)$-symmetric theory with $$ potential.

Full work available at URL: https://arxiv.org/abs/1908.11347

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