Higher dimensional supersymmetry in 4D superspace

We present an explicit formulation of supersymmetric Yang-Mills theories from \D= 5 to 10 dimensions in the familiar \N=1,\D=4 superspace. This provides the rules for globally supersymmetric model building with extra dimensions and in particular allows us to simply write down $\N=1$ SUSY preserving interactions between bulk fields and fields localized on branes. We present a few applications of the formalism by way of illustration, including supersymmetric ``shining'' of bulk fields, orbifolds and localization of chiral fermions, anomaly inflow and super-Chern-Simons theories.Comment: Typos corrected. Added reference to early work by Marcus, Sagnotti and Siegel and a term to the non-Abelian Lagrangian for D>5 formally needed for gauge invariance. The results however remain unchange

The Momentum Amplituhedron

In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in N = 4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron M n,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.Peer reviewedFinal Published versio

On the AdS/CFT Dual of Deconstruction

We consider a class of non-supersymmetric gauge theories obtained by orbifolding the N=4 super-Yang-Mills theories. We focus on the resulting quiver theories in their deconstructed phase, both at small and large coupling, where a fifth dimension opens up. In particular we investigate the r\^ole played by this extra dimension when evaluating the rectangular Wilson loops encoding the interaction potential between quarks located at different points in the orbifold. The large coupling potential of the deconstructed quiver theory is determined using the AdS/CFT correspondence and analysing the corresponding minimal surface solution for the dual gravitational metric. At small coupling, the potential between quarks decreases with their angular distance while at strong coupling we find a linear dependence at large distance along the (deconstructed) fifth dimension.Comment: 19 pages, 3 figure

Flavor at the TeV Scale with Extra Dimensions

Theories where the Standard Model fields reside on a 3-brane, with a low fundamental cut-off and extra dimensions, provide alternative solutions to the gauge hierarchy problem. However, generating flavor at the TeV scale while avoiding flavor-changing difficulties appears prohibitively difficult at first sight. We argue to the contrary that this picture allows us to lower flavor physics close to the TeV scale. Small Yukawa couplings are generated by ``shining'' badly broken flavor symmetries from distant branes, and flavor and CP-violating processes are adequately suppressed by these symmetries. We further show how the extra dimensions avoid four dimensional disasters associated with light fields charged under flavor. We construct elegant and realistic theories of flavor based on the maximal U(3)^5 flavor symmetry which naturally generate the simultaneous hierarchy of masses and mixing angles. Finally, we introduce a new framework for predictive theories of flavor, where our 3-brane is embedded within highly symmetrical configurations of higher-dimensional branes.Comment: 40 pages, 8 figure