Apparent Fine Tunings for Field Theories with Broken Space-Time Symmetries

: We exhibit a class of eﬀective ﬁeld theories that have hierarchically small Wilson coeﬃcients for operators that are not protected by symmetries but are not ﬁnely tuned. These theories possess bounded target spaces and vacua that break space-time symmetries. We give a physical interpretation of these theories as generalized solids with open boundary conditions. We show that these theories realize unusual RG ﬂows where higher dimensional (seemingly irrelevant) operators become relevant even at weak coupling. Finally, we present an example of a ﬁeld theory whose vacuum energy relaxes to a hierarchically small value compared to the UV cut-oﬀ.