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The Hierarchy problem and new dimensions at a millimeter
Abstract We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions becomeExpand
The String landscape, black holes and gravity as the weakest force
We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1)Expand
What is the simplest quantum field theory?
Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however beenExpand
A duality for the S matrix
We propose a dual formulation for the S Matrix of $$ \mathcal N $$ = 4 SYM. The dual provides a basis for the “leading singularities” of scattering amplitudes to all orders in perturbation theory,Expand
Scattering Amplitudes and the Positive Grassmannian
We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physicalExpand
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
We give an explicit recursive formula for the all ℓ-loop integrand for scattering amplitudes in $ \mathcal{N} = 4 $ SYM in the planar limit, manifesting the full Yangian symmetry of the theory. ThisExpand
Causality, analyticity and an IR obstruction to UV completion
We argue that certain apparently consistent low-energy effective field theories described by local, Lorentzinvariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded inExpand
Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC
The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work, which may also address the hierarchy problem. An example — supported by Weinberg'sExpand
New dimensions at a millimeter to a Fermi and superstrings at a TeV
Abstract Recently, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor. The gravitational and gauge interactions uniteExpand
On tree amplitudes in gauge theory and gravity
The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity inExpand