Gauge Invariance at Large Charge
| Autor: | Antipin, Oleg, Bednyakov, Alexander, Bersini, Jahmall, Panopoulos, Pantelis, Pikelner, Andrey |
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| Rok vydání: | 2022 |
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| Zdroj: | Phys.Rev.Lett. 130 (2023) 2, 021602 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.130.021602 |
| Popis: | Quantum field theories with global symmetries simplify considerably in the large-charge limit allowing to compute correlators via a semiclassical expansion in the inverse powers of the conserved charges. A generalization of the approach to gauge symmetries has faced the problem of defining gauge-independent observables and, therefore, has not been developed so far. We employ the large-charge expansion to calculate the scaling dimension of the lowest-lying operators carrying $U(1)$ charge $Q$ in the critical Abelian Higgs model in $D=4-\epsilon$ dimensions to leading and next-to-leading orders in the charge and all orders in the $\epsilon$ expansion. Remarkably, the results match our independent diagrammatic computation of the three-loop scaling dimension of the operator $\phi^Q(x)$ in the Landau gauge. We argue that this matching is a consequence of the equivalence between the gauge-independent dressed two-point function of Dirac type with the gauge-dependent two-point function of $\phi^Q(x)$ in the Landau gauge. We, therefore, shed new light on the problem of defining gauge-independent exponents which has been controversial in the literature on critical superconductors as well as lay the foundation for large-charge methods in gauge theories. Comment: LaTeX 6 pages, 1 figure, 1 table; v2: minor corrections, matches published version |
| Databáze: | arXiv |
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