Causality, renormalizability and ultra-high energy gravitational scattering

The amplitude A(s,t) for ultra-high energy scattering can be found in the leading eikonal approximation by considering propagation in an Aichelburg-Sexl gravitational shockwave background. Loop corrections in the QFT describing the scattered particles are encoded for energies below the Planck scale in an effective action which in general exhibits causality violation and Shapiro time advances. In this paper, we use Penrose limit techniques to calculate the full energy dependence of the scattering phase shift Theta_scat(hat_s},, where the single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact parameter b, for a range of scalar QFTs in d dimensions with different renormalizability properties. We evaluate the high-energy limit of Theta_scat(hat_s) and show in detail how causality is related to the existence of a well-defined UV completion. Similarities with graviton scattering and the corresponding resolution of causality violation in the effective action by string theory are briefly discussed.Comment: 23 page

Photon-graviton mixing in an electromagnetic field

Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic field. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism for obtaining an exact integral representation for the one-loop corrections to this amplitude due to scalars and fermions. We study the structure of this amplitude, and obtain exact expressions for various limiting cases.Comment: 13 pages, 1 figure, talk given by C. Schubert at QFEXT07, Leipzig, 17-21 Sep 2007, final published version (slightly extended

The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.Comment: 54 pages, 19 figures, corrected some signs in formulae and graph

Renormalization group flow with unstable particles

The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function of the renormalization group flow parameter. This allows to identify the corresponding conformal field theories together with their operator content when the unstable particles vanish from the particle spectrum. The specific model considered is the $SU(3)_{2}$-homogeneous Sine-Gordon model.Comment: 5 pages Latex, 3 figure

Decoherence and CPT Violation in a Stringy Model of Space-Time Foam

I discuss a model inspired from the string/brane framework, in which our Universe is represented as a three brane, propagating in a bulk space time punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the bulk, the D-particles cross it, and from an effective observer on D3 the situation looks like a ``space-time foam'' with the defects ``flashing'' on and off (``D-particle foam''). The open strings, with their ends attached on the brane, which represent matter in this scenario, can interact with the D-particles on the D3-brane universe in a topologically non-trivial manner, involving splitting and capture of the strings by the D0-brane defects. Such processes are described by logarithmic conformal field theories on the world-sheet. Physically, they result in effective decoherence of the string matter on the D3 brane, and as a result, of CPT Violation, but of a type that implies an ill-defined nature of the effective CPT operator. Due to electric charge conservation, only electrically neutral (string) matter can exhibit such interactions with the D-particle foam. This may have unique, experimentally detectable, consequences for electrically-neutral entangled quantum matter states on the brane world, in particular the modification of the pertinent EPR Correlation of neutral mesons in a meson factory.Comment: 41 pages Latex, five eps figures incorporated. Uses special macro