On-shell diagrams for theories with N < 4 supersymmetries

Supersymmetry breaking through transparent extra dimensions

“…A solution to this problem which would be very natural in our context is to have quarks and leptons live on separate "branes" in the extra dimensions. The separation forbids direct local couplings between quarks and leptons, and proton decay via X and Y gauge bosons would be exponentially suppressed by the massive Yukawa propagators of X and Y propagating between the quark-and lepton branes [19,20]. iv.…”

“…By approximating the sum with an integral we have assumed large volume (L > 1/ √ q 2 ). Performing the sum exactly is straightforward [22] but not necessary for our purposes.…”

Yukawa hierarchies from split fermions in extra dimensions

“…Traditional explanations of this Yukawa hierarchy invoke new symmetries, but in [1] Arkani-Hamed and Schmaltz suggested an explanation which does not require imposing new symmetries. They suggest that the hierarchies present in the Yukawa couplings of the standard model can be explained as a result of the slight displacement of the standard model field wavefunctions inside a four-dimensional domain wall in a higher-dimensional space.…”

Constructing amplitudes from their soft limits

“…The relationship between leading singularities at different loop orders, numbers of external legs and helicity configurations was studied using inverse soft in [20]. In addition, it has been shown that inverse soft reproduces tree-level maximally-helicity-violating (MHV) amplitudes and six-point next-to-MHV (NMHV) amplitudes in N = 4 sYM [15].…”

“…A recent advancement in this area due to Arkani-Hamed, et al, is a method called inverse soft which attempts to construct amplitudes from their soft limits alone [14][15][16]. Inverse soft was motivated by…”