119180615
Weyl's Gauge Invariance: Conformal Geometry, Spinors, Supersymmetry, and Interactions
Abstract We extend our program of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones for universes that are Einstein, but are novel in general backgrounds. They are generalizations of the gravitational couplings of a conformally improved scalar to fields with general scaling and tensor properties. The couplings we find are more general than just trivial ones following from a conformal compensating mechanism. In particular, in the setting where a scale gauge field (or dilaton) is included, masses correspond to Weyl weights of fields organized in “tractor” multiplets. Breitenlohner–Freedman bounds follow directly from reality of these weights. Moreover, massive, massless and partially massless theories are handled in a uniform framework. Also, bona fide Weyl invariant theories (invariant without coupling to scale) can be directly derived in this approach. The results are based on the tractor calculus approach to conformal geometry, in particular we show how to handle Fermi fields, supersymmetry and Killing spinors using tractor techniques. Another useful consequence of the construction is that it automatically produces the (anti-) de Sitter theories obtained by log-radial reduction of Minkowski theories in one higher dimension. Theories presented in detail include interacting scalars, spinors, Rarita–Schwinger fields, and the interacting Wess–Zumino model.
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.
50856545
BPS black holes, quantum attractor flows and automorphic forms
We propose a program for counting microstates of four-dimensional BPS black holes in N{>=}2 supergravities with symmetric-space valued scalars by exploiting the symmetries of timelike reduction to three dimensions. Inspired by the equivalence between the four-dimensional attractor flow and geodesic flow on the three-dimensional scalar manifold, we radially quantize stationary, spherically symmetric BPS geometries. Connections between the topological string amplitude, attractor wave function, the Ooguri-Strominger-Vafa conjecture and the theory of automorphic forms suggest that black hole degeneracies are counted by Fourier coefficients of modular forms for the three-dimensional U-duality group, associated to special unipotent representations which appear in the supersymmetric Hilbert space of the quantum attractor flow.
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.
16066542
Spinors on manifolds with boundary: APS index theorems with torsion
Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS η invariant in the presence of torsion. The bulk contribution must also be modified and is computed using a supersymmetric quantum mechanics representation. Here we find agreement with existing results which employed heat kernel and Pauli-Villars techniques. Nonetheless, this computation also provides a stringent check of the Feynman rules of de Boer et al. for the computation of quantum mechanical path integrals. Our results can be verified via a duality relation between manifolds admitting a Killing-Yano tensor and manifolds with torsion. As an explicit example, we compute the indices of Taub-NUT and its dual constructed using this method and find agreement for any finite radius to the boundary. We also suggest a resolution to the problematic appearance of the Nieh-Yan invariant multiplied by the regulator (mass) 2 in computations of the chiral gravitational anomaly coupled to torsion.
7032725
Matrix theory and Feynman diagrams
We briefly review the computation of graviton and antisymmetric tensor scattering amplitudes in Matrix Theory from a diagramatic S-Matrix point of view.
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.