119103201
A continuous Wick rotation for spinor fields and supersymmetry in Euclidean space
We obtain a continuous Wick rotation for Dirac, Majorana and Weyl spinors $\psi \to \exp ({1\over 2} \theta \gamma^4 \gamma^5)\psi$ which interpolates between Minkowski and Euclidean field theories.
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.
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.
17902636
Milne and Torus Universes Meet
Three dimensional quantum gravity with torus universe, T^2xR topology is reformulated as the motion of a relativistic point particle moving in an Sl(2,Z) orbifold of flat Minkowski spacetime. The latter is precisely the three dimensional Milne Universe studied recently by Russo as a background for Strings. We comment briefly on the dynamics and quantization of the model.
118396139
Local unit invariance, back-reacting tractors and the cosmological constant problem
When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.
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.
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.
119317491
Is Quantum Gravity a Chern{Simons Theory?
We propose a model of quantum gravity in arbitrary dimensions dened in terms of the BV quantization of a supersymmetric, innite dimensional matrix model. This gives an (AKSZ-type) Chern{Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert spaceH. The model is motivated by previous attempts to formulate gravity in terms of non-commutative, phase space, eld theories as well as the Feerman{ Graham curved analog of Dirac spaces for conformally invariant wave equations. The eld