Renormalization Group Flows, Line Defects and, the g−theorem

An important application of the study of Renormalization Group flows is in the presence of a line defect [1]. Particularly useful are the existence of charges that do not renormalize along the flow or that are monotonically decreasing as they allow us to study both strongly and weekly interacting theories. In this work, we describe those that are monotonic as they bring beautiful physical consequences such as screening , flow irreversibility, entropy, etc. The existence of such charges, initially explored by Zamolodchikov [2] in the celebrated c−theorem and later extended to higher dimensions by Komagordoski et. al. [3], has lately been extended to theories in the presence of non-local observables. In this case, in the presence of a line defect, a g−theorem [4, 5] was presented by Cuomo, Komargodski, and Raviv-Moshe. We focus on how RG flows are useful to study these theories and provide a proof of the c−and g−theorems.