15701670
D = 11 SUGRA as the low energy effective action of matrix theory: three form scattering
We employ the LSZ reduction formula for matrix theory introduced in our earlier work to compute the t-pole S-matrix for three form--three form scattering. The result agrees completely with tree level D = 11 SUGRA. Taken together with previous results on graviton-graviton scattering this shows that matrix theory indeed reproduces the bosonic sector of the D = 11 SUGRA action including the Chern-Simons term. Furthermore we provide a detailed account of our framework along with the technology to compute any matrix theory one-loop t-pole scattering amplitude at vanishing p− exchange.
16060426
Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz’s wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p, Q) = (2, 0) corresponds to a deformed Jacobi group and describes Lichnerowicz’s original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p, Q) = (0, 1) is simply the $${\mathcal N} = 1$$ superparticle whose supercharge amounts to the Dirac operator acting on spinors. The (2p, Q) = (0, 2) model is the $${\mathcal N} = 2$$ supersymmetric quantum mechanics corresponding to differential forms. (This latter pair of models are supersymmetric on any Riemannian background.) When Q is odd, the models apply to spinor-tensors. The (2p, Q) = (2, 1) model is distinguished by admitting a central Lichnerowicz-Dirac operator when the background is constant curvature. The new supersymmetric models are novel in that the Hamiltonian is not just a square of super charges, but rather a sum of commutators of supercharges and commutators of bosonic charges. These models and superalgebras are a very useful tool for any study involving high rank tensors and spinors on manifolds.
5028777
Quantum cosmology and conformal invariance.
According to Belinsky, Khalatnikov, and Lifshitz, gravity near a spacelike singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini, and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the Universe is the zero-energy eigenmode of the Hamiltonian, or the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models with enhanced ADE symmetry is constructed, based on the quantization of nilpotent coadjoint orbits.
118704552
Massive higher spins from BRST and tractors
Abstract We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit systems manifest. In this approach, physical models are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive models can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk–boundary correspondence.
119274374
Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
Fefferman and Graham showed some time ago that four dimensional conformal
 geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries
 admitting a closed homothety. Recently it was shown how conformal geometry provides a
 description of physics manifestly invariant under local choices of unit systems.
 Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale
 tractor (a six component vector subject to a certain first order covariant constancy
 condition at every point in four dimensional spacetime). These results suggest a six
 dimensional description of four dimensional physics, a viewpoint promulgated by the two
 times physics program of Bars. The Fefferman--Graham construction relies on a triplet of
 operators corresponding, respectively to a curved six dimensional light cone, the dilation
 generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first
 class algebra of constraints in a six-dimensional gauge theory. In this article four
 dimensional gravity is recast in terms of six dimensional quantum mechanics by melding the
 two times and tractor approaches. This "parent" formulation of gravity is built from an
 infinite set of six dimensional fields. Successively integrating out these fields yields
 various novel descriptions of gravity including a new four dimensional one built from a
 scalar doublet, a tractor vector multiplet and a conformal class of metrics.
11655832
Automorphic Forms: A Physicist's Survey
These Notes are an introduction to automorphic forms, from a physicist viewpoint. Basic concepts are introduced via the simple $Sl(2)$ Eisenstein and Jacobi theta series. The general construction of continuous representations and of their accompanying Eisenstein series is detailed for $Sl(3)$. Thereafter we present nilpotent representations and their theta series for arbitrary simply-laced groups based on our recent work. New results results on the geometrical interpretation of minimal representations are included, implying e.g. that $E_6$ acts on SO(5,5) pure spinors. We close with comments about applications of automorphic forms to the supermembrane and to quantum cosmology.
11049353
Covariant constraints for generic massive gravity and analysis of its characteristics
We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates 5 degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. The constraint’s covariant expression permits computation of the model’s caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.
119108691
Combining neutrino oscillation experiments with the Feldman–Cousins method
In this paper we describe how two or more experimental results can be combined within the procedure of Feldman and Cousins, to provide combined confidence limits on the physical parameters of interest. We demonstrate the technique by combining the recent electron neutrino appearance results from T2K and MINOS. Our best fit point is sin2 2θ13 = 0.08 (0.11) and δ = 1.1 (2.0)π; in addition we exclude sin2 2θ13 = 0 at 2.7σ (2.8σ) for the normal (inverted) neutrino mass hierarchy.