Abstract
We investigate defects in scalar field theories in four and six dimensions in a double-scaling (semiclassical) limit, where bulk loops are suppressed and quantum effects come from the defect coupling. We compute β-functions up to four loops and find that fixed points satisfy dimensional disentanglement — i.e. their dependence on the space dimension is factorized from the coupling dependence — and discuss some physical implications. We also give an alternative derivation of the β functions by computing systematic logarithmic corrections to the Coulomb potential. In this natural scheme, β functions turn out to be a gradient of a ‘Hamiltonian’ function \( \mathcal{H} \). We also obtain closed formulas for the dimension of scalar operators and show that instabilities do not occur for potentials bounded from below. The same formulas are reproduced using Rigid Holography.
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Acknowledgments
J.G.R. acknowledges financial support from projects MINECO grant PID2019-105614GB- C21, and from the State Agency for Research of the Spanish Ministry of Science and Inn ovation through the “Unit of Excellence María de Maeztu 2020-2023” (CEX2019-000918-M). The work of I.C.B. and D.R.G is partly supported by Spanish national grant MCIU-22-PID2021-123021NB-I00 as well as the Principado de Asturias grant SV-PA-21- AYUD/2021/52177.
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Carreño Bolla, I., Rodriguez-Gomez, D. & Russo, J.G. RG flows and stability in defect field theories. J. High Energ. Phys. 2023, 105 (2023). https://doi.org/10.1007/JHEP05(2023)105
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DOI: https://doi.org/10.1007/JHEP05(2023)105