Scientific Series

In causal set quantum gravity, spacetime is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal set. After giving a brief review of causal sets, I will discuss two distinct approaches to constructing a quantum dynamics for causal sets. In the first approach one borrows heavily from the continuum to construct a partition function for causal sets. This is illustrated in a 2-d model of causal sets, in which typicality replaces quantum probabilities. The second approach is intrinsic, and uses the quantum measure formulation in which dynamics is described in the language of measure theory and observables are measurable sets in an event algebra. Using the example of complex percolation dynamics I will show that naive attempts to carry out this process for the quantum measure may not work. I will end by discussing possible ways to address this question.

Quantum Bayesianism is a point of view on quantum foundations that says that there is no such thing as a “measurement problem” because there is no such THING as a quantum state: Quantum states are not things---instead information. But the view doesn’t stop there; it starts there! Taking the idea seriously over the last 15 years has been the direct motivation for a number of theorems and objects in quantum information theory: from the no-broadcasting theorem, to the quantum de Finetti theorem, and even some quantum cryptographic alphabets. I will review some of this, and then move on to the holy grail of present efforts: Finding an efficient representation of quantum states in terms of a singular probability function. Doing so leads to the hard technical problem of demonstrating the existence of a certain very symmetric sets of quantum states, and holds out the hope of understanding the amount of “quantum stuff” in a physical system in terms of a single parameter. (I.e., there is the THING that the quantum state is not).

In the Scholium in Newton's Principia which contains the discussions about absolute space, time, and the bucket experiment, Newton also posed a problem that Julian Barbour has denoted the "Scholium problem". Newton writes there "But how are we to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it". This problem was clearly considered very important by Newton who claims he wrote the Principia dedicated to this problem. Interestingly Newton never returned to the problem. In this talk we are going to give a mathematical precise formulation of the Scholium problem. A subpart of the Scholium problem consists of determining how accurate the observers clock is. We are going to start from that end and see that the problem of defining duration is inseparately intertwined with the full scholium problem.

We report on a new class of fast-roll inflationary models. In a part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the behavior of the perturbations around this quasi-de Sitter background is dual to a quantum field theory in flat space-time. Finally, the form of the primordial power spectrum is determined by the interaction between different modes of scalar perturbations.

I will review the progress made in our understanding of the QCD phase diagram within an RG approach to QCD and effective QCD models. In particular this includes a discussion of the confinement-deconfinement phase transition/cross-over, the chiral phase transition/cross-over, as well as their interrelation.

The concept of renormalization lies at the heart of fundamental physics. I introduce in this talk the Connes-Kreimer algebraic approach for expressing renormalizability in quantum field theories as well as the extension of these notions to the manifestly non-local framework of noncommutative quantum field theories. Finally, I will present an attempt to further generalize these concepts to quantum gravity models. based on: 0909.5631 [gr-qc], Class. Quant. Grav. (in press)

In recent years the characterization of many-body ground states via the entanglement of their wave-function has attracted a lot of attention. One useful measure of entanglement is provided by the entanglement entropy S. The interest in this quantity has been sparked, in part, by the result that at one dimensional quantum critical points (QCPs) S scales logarithmically with the subsystem size with a universal coefficient related to the central charge of the conformal field theory describing the QCP. On the other hand, in spatial dimension d > 1 the leading contribution to the entanglement entropy scales as the area of the boundary of the subsystem. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a QCP, S is believed to possess subleading universal corrections. In this talk, I will present the first field-theoretic study of entanglement entropy in dimension d > 1 at a stable interacting QCP - the quantum O(N) model. Our results confirm the presence of universal corrections to the entanglement entropy and exhibit a number of surprises such as different epsilon -> 0 limits of the Wilson-Fisher and Gaussian fixed points, violation of large N counting and subtle dependence on replica index.

Self-assembly refers to any thermodynamic process in which a bunch of particles (molecules, biomolecules, polymers, colloids) come together in solution to form an ordered structure. In living things it is a widely used and robust manufacturing tool: DNA, RNA and proteins spontaneously form three dimensional structures, and supramolecular structures emerge from protein aggregates with staggering degrees of ordering and specificity. By contrast, most synthetic systems in soft condensed matter do not assemble robustly. In this talk I will discuss experiments on simple systems that allow us to probe the physics and thermodynamics of self-assembly. We use systems consisting of small numbers (N ⇐ 12) of confined spherical colloidal particles to understand what physical parameters (interactions) determine how a system will assemble. We find that the probability of self-assembling a particular configuration can be understood in terms of the geometry of sphere packings. The geometrical model gives some insights into how phase transitions emerge as N approaches the bulk limit. At the same time, it yields some general insights into the design principles for robust self-assembly.

Primordial non-Gaussianity has been traditionaly constrained using three-point function of the cosmic microwave background. Two years ago, however, Dalal et al have shown that non-Gaussianity of the local type induces a scale dependent bias for biased tracers of the underlying dark matter structure. This allows constraining of the primordial non-Gaussianity from measurements of large-scale structure provided by redshift surveys. I will discuss the technique, its theoretical aspects, it surprising resilience towards systematics and current results from the real data. I will also show some preliminary new results: extension to the two field inflationary models and the analogue of the Dalal effect in the Lyman alpha forest.

F-theory based vacua provide a potentially promising starting point for realizing Grand Unified Theories (GUTs) in string theory. In minimal realizations of this framework based on a point of E8 unification, this turns out to be quite constraining, and leads to specific expectations for the form of supersymmetry breaking. We discuss how the parameters of the F-theory GUT determine the sparticle spectrum, and possible signatures at the LHC.

We show that when a volume of quark matter rotates, there is an axial current flowing along the rotation axis. This effect has been overlooked in all previous treatments of relativistic fluids until calculations using gauge/gravity duality indicate it existence. The effect is a manifestation of triangle anomalies, and may exhibit itself in heavy ion collisions with nonzero impact parameter.