Extra Dimensions & Fuzzy Branes in String-Inspired Nonlocal Field Theory

Abstract

Particle physics models with extra dimensions of space (EDS's) and branes allow to shed new light on naturalness of the electroweak and flavor sectors, with a rich TeV scale phenomenology. Usually, such models are formulated in the framework of local effective field theories. The scope of this article is to propose new model building issues with EDS and branes, arising in the framework of string-inspired infinite derivative quantum field theories (QFT's), which are perturbatively exorcized (ghost-free) and intrinsically nonlocal above some ultraviolet (UV) scale. First, a toy model with bulk and brane scalar fields is presented. It is shown that a 4D field localized on a δ-like 3-brane is still delocalized in the bulk on a small distance from the brane position, with a penetration length given by the nonlocal length scale. Fields localized on such distant fuzzy branes are thus allowed to interact directly with suppressed couplings, which is impossible in a local QFT. It is also argued that above the nonlocal scale, it should be much more difficult to probe the Kaluza-Klein (KK) tower in an experiment, because of the UV opaqueness of such infinite derivative QFT's. In this way, a shadow EDS is obtained if the nonlocal and KK scales are close to each other, such that the effects of the KK-excitations are screened compared to a local QFT. After that, directions for model building are given. By using this new possibility of fuzzy branes, a new realization of split fermions in an EDS is presented, allowing to naturally generate flavor hierarchies. Moreover, with a warped EDS, the usual warp transmutation of a brane mass term is revisited, where it is shown that the nonlocal scale is also redshifted. This may provide a new way to solve or reduce the little hierarchy problem related to the Higgs boson mass.