Natural Supersymmetry in Warped Space

We explore the possibility of solving the hierarchy problem by combining the paradigms of supersymmetry and compositeness. Both paradigms are under pressure from the results of the Large Hadron Collider (LHC), and combining them allows both a higher confinement scale -- due to effective supersymmetry in the low energy theory -- and heavier superpartners -- due to the composite nature of the Higgs boson -- without sacrificing naturalness. The supersymmetric Randall-Sundrum model provides a concrete example where calculations are possible, and we pursue a realistic model in this context. With a few assumptions, we are led to a model with bulk fermions, a left-right gauge symmetry in the bulk, and supersymmetry breaking on the UV brane. The first two generations of squarks are decoupled, reducing LHC signatures but also leading to quadratic divergences at two loops. The model predicts light $W'$ and $Z'$ gauge bosons, and present LHC constraints on exotic gauge bosons imply a high confinement scale and mild tuning from the quadratic divergences, but the model is otherwise viable. We also point out that R-parity violation can arise naturally in this context.Comment: 60 pages, 7 figures; v2: minor changes, references added, published versio

Evidence for a Lattice Weak Gravity Conjecture

The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at every lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling $e$ exists, then the fundamental gravitational cutoff energy of the theory is no higher than $\sim e^{1/3} M_{\rm Pl}$.Comment: v2: 41 pages, typos fixed, references added, substantial revisions and clarifications (conclusions unchanged

The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.Comment: 50 pages, 5 figures. v2: references added, clarified remarks about Higgsin