A model for the interplay between plastic tradeoffs and evolution in changing environments.

Performance tradeoffs are ubiquitous in both ecological and evolutionary modeling, yet they are usually postulated and built into fitness and ecological landscapes. However, tradeoffs depend on genetic background and evolutionary history and can themselves evolve. We present a simple model capable of capturing the key feedback loop: evolutionary history shapes tradeoff strength, which, in turn, shapes evolutionary future. One consequence of this feedback is that genomes with identical fitness can have different evolutionary properties shaped by prior environmental exposure. Another is that, generically, the best adaptations to one environment may evolve in another. Our simple framework bridges the gap between the phenotypic Fisher's Geometric Model and the genotypic properties, such as modularity and evolvability, and can serve as a rich playground for investigating evolution in multiple or changing environments.

Two-Dimensional Non-Fermi-Liquid Metals: A Solvable Large-N Limit.

Significant effort has been devoted to the study of "non-Fermi-liquid" (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point. The problem has been extensively studied in a large-N limit (N corresponding to the number of fermion flavors) where universal behavior can be obtained by solving a set of coupled saddle-point equations. However, a remarkable study by Lee revealed the breakdown of such approximations in two spatial dimensions. We show that an alternate approach, in which the fermions belong to the fundamental representation of a global SU(N) flavor symmetry, while the order parameter fields transform under the adjoint representation (a "matrix large-N" theory), yields a tractable large N limit. At low energies, the system consists of an overdamped boson with dynamical exponent z=3 coupled to a non-Fermi-liquid with self-energy Σ(ω)∼ω^{2/3}, consistent with previous studies.

Nonsupersymmetric Dualities from Mirror Symmetry.

We study supersymmetry breaking perturbations of the simplest dual pair of (2+1)-dimensional N=2 supersymmetric field theories-the free chiral multiplet and N=2 super QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several nonsupersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these nonsupersymmetric dualities directly descend.

Effects of compactification in D-brane inflation.

In D3-brane inflation, the inflaton potential receives important contributions from sources in the compact space, such as fluxes, other D-branes, and orientifold planes. Most previous analyses have considered only the effects of sources near to the inflationary D3-brane, but in fact distant sources do not generically decouple and can critically influence the dynamics during inflation. We provide a systematic method for incorporating the effects of arbitrary distant sources as perturbations to the local supergravity background. We use this approach to obtain the structure of the potential for a D3-brane in a warped throat geometry attached to a general compact space. A significant, and well-known, contribution to this potential arises from quantum effects involved in the stabilization of the compactification volume. Our method automatically captures these effects, encoding them in a suitable flux background.