Scientific Series

Diffeomorphism symmetry is the underlying symmetry of general relativity and deeply intertwined with its dynamics. The notion of diffeomorphism symmetry is however obscured in discrete gravity, which underlies most of the current quantum gravity models. We will propose a notion of diffeomorphism symmetry in discrete models and find that such a symmetry is weakly broken in many models. This is connected to the problem of finding a consistent canonical dynamics for discrete gravity. Finally we will discuss methods to construct models with exact symmetries and elaborate on the connection between diffeomorphism symmetry and triangulation independence.

The hot, gaseous atmospheres of galaxies and clusters of galaxies are repositories for the energy output from accreting, supermassive black holes located in the nuclei of galaxies. X-ray observations show that star formation fueled by gas condensing out of hot atmospheres is strongly suppressed by feedback from active galactic nuclei (AGN). This mechanism may solve several outstanding problems in astrophysics, including the numbers of luminous galaxies and their colors, and the excess number of hot baryons in the Universe. The most energetic AGN outbursts may be powered by rapidly-spinning, ultra-massive black holes.

Stellar evolution from a protostar to neutron star is of one of the best studied subjects in modern astrophysics. Yet, it appears that there is still a lot to learn about the extreme conditions where the fundamental particle physics meets strong gravity regime. After all of the thermonuclear fuel is spent, and after the supernova explosion, but before the remaining mass crosses its own Schwarzschild radius, the temperature of the central core of the star might become higher than the electroweak symmetry restoration temperature. The source of energy, which can at least temporarily balance gravity, are baryon number violating instanton processes which are basically unsuppressed at temperatures above the electroweak scale. We constructed a solution to the Oppenheimer-Volkoff equation which describes such a star. The energy release rate is enormous at the core, but gravitational redshift and the enhanced neutrino interaction cross section at these densities make the energy release rate moderate at the surface of the star. The lifetime of this new quasi-equilibrium can be more than ten million years, which is long enough to represent a new stage in the evolution of a star.

We will give a short overview of non-perturbative quantum gravity models and discuss some key common problems for these models. In particular we will analyze what background independence requires from a theory of quantum gravity.

The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is intractable for classical computers. Such a machine would have tremendous applications in all physical sciences, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the more fundamental problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibb's states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. In this talk, I will demonstrate that the corresponding quantum problem can be solved by a quantum Metropolis algorithm. This validates the quantum computer as a universal simulator, and proves that the so-called sign problem occurring in quantum Monte Carlo methods can be resolved with a quantum computer.

We investigate a simple theory where Baryon number (B) and Lepton number (L) are local gauge symmetries. In this theory B and L are on the same footing and the anomalies are cancelled by adding a single new fermionic generation. There is an interesting realization of the seesaw mechanism for neutrino masses. Furthermore there is a natural suppression of flavour violation in the quark and leptonic sectors since the gauge symmetries and particle content forbid tree level flavor changing neutral currents involving the quarks or charged leptons. Also one finds that the stability of a dark matter candidate is an automatic consequence of the gauge symmetry. Some constraints and signals at the Large Hadron Collider are briefly discussed.

Topological phases in spin systems are exciting frontiers of research with intimate connections to quantum coding theory. However, there is a disconnection between quantum codes and the idea of topology, in the absence of geometry and physical realizability. Here, we introduce a toy model, in which quantum codes are constrained to not only have a local geometric description, but also have translation and scale symmetries. These additional physical constraints enable us to assign topologically invariant properties to geometric shapes of logical operators of the code. Topological phases of the model are analyzed by geometrically classifying logical operators. The classification scheme also has topologically universal properties which are invariant under local unitary transformations and local perturbations, and may explain how global symmetries of a system Hamiltonian give rise to topological phases in correlated spin systems.

I will present recent numerical results obtained in collaboration with Frans Pretorius that describe head-on collisions of two solitons coupled to the general relativistic gravitational field and boosted to ultra relativistic energies. The calculations show, for the first time, that at sufficiently high energies such a collision leads to black hole formation, consistent with hoop conjecture arguments. This implies that the non-linear gravitational interaction between the kinetic energy of the solitons results in gravitational collapse, and the arguments for black hole formation in super-Planck scale particle collisions are robust. I will also speculate on the nature of the threshold of black hole formation in the model.

The Wheeler delayed choice experiment, Elitzur-Vaidman interaction-free measurement, and Hosten-Kwiat counterfactual computation will be discussed to answer Bohr's forbidden question: "Where is a quantum particle while it is inside a Mach-Zehnder Interferometer?". I will argue that the naive application of Wheeler's approach fails to explain a weak trace left by the particle and that the two-state vector description is required.

Two of the most exciting observables in the cosmic microwave background (CMB) radiation, which could deeply impact our picture of the early universe, are non-Gaussianity and tensor modes. A potential detection of tensor modes can be explained in terms of a model of large field inflation. Theoretical considerations suggest that a symmetry should be invoked in order to protect the flatness of the inflaton potential and hence an axion enjoying a shift symmetry is a natural candidate. As main example, I will present a model of inflation in string theory based on axion monodromy. Non-perturbative effects typically correct the axion potential leading to small sinusoidal modulations on top of an otherwise flat slow roll potential. It can be shown analytically that a resonance between the oscillations of the background and the oscillations of the curvature fluctuations is responsible for the production of an observably large non-Gaussian signal. An explicit expression for the shape of this resonant non-Gaussianity will be presented. There is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and in fact resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. Hopefully the analytic expression for resonant non-Gaussianity will be useful to further observationally constrain this class of models.

Galaxy mergers, which are a natural consequence of hierarchical assembly of galaxies, are expected to produce binary black holes, which subsequently merge. The detection and analysis of gravitational waves from these sources is the major aim of the next generation gravitational wave detector: LISA, the Laser Interferometric Space Antenna. These gravitational waves encode a tremendous amount of information, but to make the connection with astrophysics and cosmology, it is necessary to identify the galaxies hosting these mergers via the associated electromagnetic counterpart to these mergers. I will describe these mergers events and discuss the various regimes where potential electromagnetic counterparts can be found. I will also describe some recent work, which holds much promise for the prompt identification of these mergers -- an electromagnetic precursor from tidal forcing.