SL(2,R) covariant conditions for N=1 flux vacua

Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are elegantly described by generalized complex geometry. However, this approach typically obscures the SL(2, R) covariance of the underlying theory. We show how to rewrite the pure spinor equations of Grana, Minasian, Petrini and Tomasiello (hep-th/0505212) in a manifestly SL(2,R) covariant fashion. Solutions to these equations fall into two classes: "charged" solutions, such as those containing D5-branes, and "chargeless" solutions, such as F-theory solutions in the Sen limit and AdS4 solutions. We derive covariant supersymmetry conditions for the chargeless case, allowing general SU(3)xSU(3) structure. The formalism presented here greatly simplifies the study of the ten-dimensional geometry of general supersymmetric compactifications of F-theory.Comment: 32 pages, no figures; v2: references and a minor clarification adde

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

Family-Personalized Dietary Planning with Temporal Dynamics

Poor diet and nutrition in the United States has immense financial and health costs, and development of new tools for diet planning could help families better balance their financial and temporal constraints with the quality of their diet and meals. This paper formulates a novel model for dietary planning that incorporates two types of temporal constraints (i.e., dynamics on the perishability of raw ingredients over time, and constraints on the time required to prepare meals) by explicitly incorporating the relationship between raw ingredients and selected food recipes. Our formulation is a diet planning model with integer-valued decision variables, and so we study the problem of designing approximation algorithms (i.e, algorithms with polynomial-time computation and guarantees on the quality of the computed solution) for our dietary model. We develop a deterministic approximation algorithm that is based on a deterministic variant of randomized rounding, and then evaluate our deterministic approximation algorithm with numerical experiments of dietary planning using a database of about 2000 food recipes and 150 raw ingredients

Mesino Oscillation in MFV SUSY

R-parity violating supersymmetry in a Minimal Flavor Violation paradigm can produce same-sign dilepton signals via direct sbottom-LSP pair production. Such signals arise when the sbottom hadronizes and the resulting mesino oscillates into an anti-mesino. The first bounds on the sbottom mass are placed in this scenario using current LHC results.Comment: 14 pages, 6 figure

Negative Branes, Supergroups and the Signature of Spacetime

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3 branes, we show that $SU(0|N)$ supergroup theories are holographically dual to an exotic variant of type IIB string theory on $dS_{3,2} \times \bar S^5$, for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $\mathcal N=2 ~SU(N|M)$ gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.Comment: 66 pages, 12 figures. V2: additional references, minor typo correction

Minimal continuum theories of structure formation in dense active fluids

Self-sustained dynamical phases of living matter can exhibit remarkable similarities over a wide range of scales, from mesoscopic vortex structures in microbial suspensions and motility assays of biopolymers to turbulent large-scale instabilities in flocks of birds or schools of fish. Here, we argue that, in many cases, the phenomenology of such active states can be efficiently described in terms of fourth- and higher-order partial differential equations. Structural transitions in these models can be interpreted as Landau-type kinematic transitions in Fourier (wavenumber) space, suggesting that microscopically different biological systems can share universal long-wavelength features. This general idea is illustrated through numerical simulations for two classes of continuum models for incompressible active fluids: a Swift-Hohenberg-type scalar field theory, and a minimal vector model that extends the classical Toner-Tu theory and appears to be a promising candidate for the quantitive description of dense bacterial suspensions. We also discuss briefly how microscopic symmetry-breaking mechanisms can enter macroscopic continuum descriptions of collective microbial motion near surfaces and conclude by outlining future applications.Comment: 22 pages, 6 figures, text extended, App A added, references updated/adde