RG flows and stability in defect field theories

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 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.