The ABJM Amplituhedron

In this paper, we take a major step towards the construction and applications of an all-loop, all-multiplicity amplituhedron for three-dimensional planar $\mathcal{N}=6$ Chern-Simons matter theory, or the $\textit{ABJM amplituhedron}$. We show that by simply changing the overall sign of the positive region of the original amplituhedron for four-dimensional planar $\mathcal{N}=4$ super-Yang-Mills (sYM) and performing a symplectic reduction, only three-dimensional kinematics in the middle sector of even-multiplicity survive. The resulting form of the geometry, combined with its parity images, gives the full loop integrand. This simple modification geometrically enforces the vanishing of odd-multiplicity cuts, and manifests the correct soft cuts as well as two-particle unitarity cuts. Furthermore, the so-called ``bipartite structures" of four-point all-loop negative geometries also directly generalize to all multiplicities. We introduce a novel approach for triangulating loop amplituhedra based on the kinematics of the tree region, resulting in local integrands tailored to ``prescriptive unitarity". This construction sheds fascinating new light on the interplay between loop and tree amplituhedra for both ABJM and $\mathcal{N}=4$ sYM: the loop geometry demands that the tree region must be dissected into $\textit{chambers}$, defined by the simultaneous positivity of maximal cuts. The loop geometry is then the ``fibration" of the tree region. Using the new construction, we give explicit results of one-loop integrands up to ten points and two-loop integrands up to eight points by computing the canonical form of ABJM loop amplituhedron.Comment: 60 pages + many figures; v2: minor changes. Version to appear in JHE

Fracture Behavior of Alumina/Monazite Multilayer Laminates

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65994/1/j.1151-2916.2000.tb01278.x.pd

Divergent nematic susceptibility in an iron arsenide superconductor

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature.Comment: 8 pages, 8 figure

Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron

We elaborate on aspects of a new positive geometry proposed recently, which was conjectured to be the four-point amplituhedron for ABJM theory. We study generalized unitarity cuts from the geometry, and in particular we prove that (1) the four-point integrand satisfies perturbative unitarity (or optical theorem) to all loops, which follows directly from the geometry, and (2) vanishing cuts involving odd-point amplitudes follow from the ``bipartite" nature of the associated ``negative geometries", which justifies their appearance in ABJM theory. We also take a first step in integrating the forms of these negative geometries and obtain an infrared-finite quantity up to two loops, from which we extract the cusp anomalous dimension at leading order.Comment: 21 pages, many figures,minor change