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High Energy Physics - Theory
Title: RG Flows and Stability in Defect Field Theories
(Submitted on 3 Mar 2023 (v1), last revised 14 Aug 2023 (this version, v4))
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 $\beta $-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 $\beta$ functions by computing systematic logarithmic corrections to the Coulomb potential. In this natural scheme, $\beta $ functions turn out to be a gradient of a `Hamiltonian' function ${\cal H}$. 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.
Submission history
From: Ignacio Carreño Bolla [view email][v1] Fri, 3 Mar 2023 14:04:56 GMT (55kb,D)
[v2] Mon, 13 Mar 2023 08:29:14 GMT (55kb,D)
[v3] Tue, 16 May 2023 13:42:03 GMT (111kb,D)
[v4] Mon, 14 Aug 2023 09:30:22 GMT (55kb,D)
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