Research in the Particle Theory group

(Tim Hollowood, Prem Kumar, Graham Shore)

Our recent research on quantum field theory in curved spacetime has focused on fundamental principles, notably the realisation of causality and unitarity in theories apparently exhibiting superluminal propagation.

This has led to the discovery or improved understanding of many key effects of spacetime geometry in QFT which arise only at quantum loop level, including: (i) the essential role of the Penrose limit in the analysis of quantum propagation, (ii) a novel analytic structure of Green functions arising from the geometry of geodesic congruences, violating several fundamental assumptions of S-matrix theory and dispersion relations, (iii) the existence of below-threshold decays, and (iv) the possibility of real-time renormalization of quantum fields propagating in gravitational backgrounds.

The effect of gravitational tidal forces acting on the virtual cloud of electron-positron pairs surrounding a photon propagating in curved spacetime has been studied in detail. This endows spacetime with a non-trivial refractive index exhibiting remarkable properties unique to gravitational theories, including superluminal low-frequency propagation, in apparent violation of causality, and amplification of the photon field amplitude, in apparent violation of unitarity. The latter effect necessitated the reformulation of the optical theorem in curved spacetime, showing that the usual positivity constraint on the imaginary part of amplitudes, normally considered an essential consequence of unitarity, only holds globally while locally manifest positivity is lost. This has potentially wide-reaching implications for quantum theories involving gravity.

For their review of this work, focusing on the behaviour of quantum fields near a spacetime singularity, Hollowood and Shore were awarded Third Prize in the 2012 Gravity Research Foundation Essay Competition.

The behaviour of quantum fields in curved spacetime can also be investigated using the techniques of string theory and gauge-gravity duality (or holography). Specifically, strongly interacting quantum fields on a fixed de Sitter spacetime can be shown to be dual to gravity on asymptotically AdS spacetimes along with a horizon behind which the spacetime experiences a cosmological 'Big Crunch' singularity. Properties of crunching geometries are being investigated by Kumar and PhD students, using techniques from the AdS/CFT correspondence, the eventual goal being to understand whether such cosmological singularities can be smoothed out by string theory effects.