Scientific Series

General relativity is invariant under diffeomorphisms, and

excitations of the metric corresponding to diffeomorphisms

are nonphysical.  In the presence of a boundary, though --

including a boundary at infinity -- the Einstein-Hilbert

action with suitable boundary terms is no longer fully

invariant, and certain diffeomorphisms are promoted to

physical degrees of freedom.  After briefly describing how

this happens in (2+1)-dimensional AdS gravity, I will

report on work in progress on the asymptotically flat case,

for which the newly dynamical diffeomorphisms are the

superrotations, and the boundary action is related to

coadjoint orbits of the Virasoro group and Hill's equation.

Current observations provide precise but limited information about inflation and reheating. Theoretical considerations, however, suggest that the early universe might be filled with a large number of interacting fields with unknown interactions.  How can we quantitatively understand the dynamics of perturbations during inflation and reheating in such scenarios and when only limited

constraints are available from observations?   Based on a precise

mapping between particle production in cosmology to resistivity in disordered, quasi one-dimensional wires, I will provide a statistical framework to resolve such seemingly intractable calculations. A number of phenomenon in disordered wires find an analogue in particle production. For example, Anderson localization in quasi one-dimensional wires can be directly mapped to exponential particle production in the early universe. The talk will be focussed on the general framework and some toy examples, though in the end I will discuss possible (future) applications to calculating observables.

Spectral distortions of the CMB provide a powerful new probe of early Universe processes. Even if so far no average spectral distortion has been seen, LCDM does predict several signals that are within reach of current technology. In this talk, I will give a broad brush overview of our most recent understanding of the formation and evolution of distortions in the early Universe, highlighting guaranteed LCDM signals and what we hope to learn from them about the Universe we live in.

We present results from a study of Euclidean dynamical triangulations in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior, and that once this tuning is performed, our simulations provide evidence in support of the asymptotic safety scenario for gravity.  We discuss our motivation for the tuning and present our numerical results. Finally, we discuss what our simulations imply for the dimension of the ultraviolet critical surface, which sets the number of free parameters in the theory.

Recent developments in our understanding of black hole evaporation and the information paradox suggest that effects from quantum gravity are not necessarily hidden at the Planck scale. They might even one day be testable by gravitational wave measurements. To prepare ourselves, we must first understand what quantum gravity really means. Thankfully, we are pre-armed with a deep principle about gravity—that spacetime is really a hologram—and a powerful model for making this idea precise: gauge/gravity duality. The present challenge is to translate our questions about gravity into the natural language of the dual conformal field theory (CFT). I will describe the foundation for such a program that links the integral geometry of a gravitational spacetime to a CFT operator product expansion.

As discussed in last week’s colloquium, the use of the p-adic metric in state space provides a route to resolving the Bell Theorem in favour of realism and local causality, without fine tuning. Here the p-adic integers provide a natural way to describe the fractal geometry of Invariant Set Theory’s state space. In this talk I first explore the role of complex numbers in Invariant Set Theory (arXiv:1605.01051), and describe a novel realistic perspective on quantum interferometry. Then I will describe a programme of work to synthesise quantum and gravitational physics realistically and causally within the framework of Invariant Set Theory. I will describe a p-adic generalisation of the field equations of General Relativity, and discuss the consequent novel perspectives for understanding the dark (energy and matter) universe. 

We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric N=4 Yang-Mills theory, three-dimensional conformal field theories and QCD.

An unbroken U(1)' is a minimal possibility for a dark matter self interaction, and may even be associated with dark matter stability. However, such an interaction faces incredibly strong constraints due to collective plasma effects, which dominate over 2-to-2 scattering by an order-of-magnitude of orders-of-magnitude. I will discuss the physics of these collective effects, and show preliminary results of simulation. The constraint of such a self interaction is estimated to be nearly as weak as gravity. 

Gravitational lensing by matter clumps can magnify various transient bursts in the sky, making them more detectable from the high redshift Universe. For one example, chirping gravitational waves from stellar-mass black hole binary mergers, as first detected by LIGO recently, can appear louder due to intervening galaxies. In the absence of electromagnetic counterpart, as I will discuss, lensing magnification can bias the determination of binary mass and redshift, which needs to be corrected for when testing source evolution and formation models through event statistics. As another example, compact dark matter of masses 10-100 solar masses can gravitationally lens fast radio bursts, creating double-peaked time-domain signature with a resolvable time delay on the order of milliseconds. I discuss that forthcoming fast radio burst surveys can directly probing this interesting mass range for compact dark matter by detecting 10^4 bursts per year.

In the last few years, we have made remarkable progress in understanding the properties of our observable Universe which appears to have evolved from a hot Big Bang 13.7 billion years ago. The fine-tuning of initial conditions required to reproduce our present day Universe suggests that our Universe may merely be a region within an eternally inflating super-region. Many other regions could exist beyond our observable Universe with each such region governed by a different set of physical parameters than the ones we have measured for our Universe. Collision between these regions, if they occur, should leave signatures of anisotropy in the cosmic microwave background. I will present our analysis of the Planck data which had led to the detection of spectral anisotropies at the location of some high-latitude cold spots associated with the CMB. I will argue that the excess emission may be due to enhanced Hydrogen Paschen-series emission from the epoch of recombination. The strength of the emission would favor a collision with an alternate Universe with a much higher baryon to photon ratio than our own and suggest an anthropic explanation for the value of the cosmological constant. Future, observational tests of this hypothesis will also be discussed.

We numerically investigate the expansion of clouds of hard-core bosons in a 2D square lattice using a matrix-product state based method. This non-equilibrium setup is induced by quenching a trapping potential to zero and is specifically motivated by an experiment with ultracold atoms [1]. As the anisotropy for hopping amplitudes in different spatial directions is varied from 1D to 2D, we observe a crossover from a fast ballistic expansion in the 1D limit to much slower dynamics in the isotropic 2D lattice [2].

Introducing a site-dependent disorder potential allows to study many body localization (MBL). In a very recent experiment, the melting of a domain wall gave evidence for an MBL transition in 2D [3]. We study 1D and quasi-1D models, for which the phase diagram in the presence of disorder is known, such as the Anderson insulator, Aubry-Andre model and interacting fermions in 1D and on a two-leg ladder [4]. By considering several observables, we demonstrate that the domain wall melting can indeed yield quantitative information on the transition from an ergodic to the MBL phase as a function of disorder.

[1] J. P. Ronzheimer et al., PRL 110, 205301 (2013) [2] J. Hauschild et al., PRA 92, 053629 (2015) [3] J. Choi et al., arXiv:1604.04178 (2016) [4] J. Hauschild et al., in preparation