Defects in scalar field theories, rg flows and dimensional disentangling

D.R-G. thanks the CERN Theory Division for warm hospitality as this work was being finished. He also thanks the organizers of the Large charge at Les Diablerets meeting (as well as to SwissMAP) for a very stimulating environment where part of this work was carried out. D.R-G. is partially supported by the Spanish government grant MINECO-16- FPA2015-63667-P. He also acknowledges support from the Principado de Asturias through the grant FC-GRUPIN-IDI/2018/000174. 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 Innovation through the “Unit of Excellence María de Maeztu 2020-2023” (CEX2019-000918-M).