Quantum Gravity

This talk will deal with a new connection formulation for higher-dimensional (Super)gravity theories and its applications. We will start by reviewing the basic ideas of loop quantum gravity. Next, the derivation of the new connection formulation will be discussed and it will be shown that the quantization methods developed in the context of loop quantum gravity apply. We comment on applications of the framework, focusing on making contact with String theory.

The parity invariance of spinfoam gravity is an open question. Naively, parity breaking should reside in the sign of the Immirzi parameter. I show that the new Lorentzian vertex formula is in fact independent of this sign, suggesting that the dynamics is parity-invariant. The situation with boundary states and operators is more complicated. I discuss parity-related pieces of the transition amplitude and graviton propagator in the large-spin 4-simplex limit. Numerical results indicate patterns similar to those in the Euclidean case. In particular, parity-related components of the graviton propagator differ by a phase. I discuss possible resolutions of this issue.

We provide a microscopic understanding of the nucleation of topological quantum liquids that arise due to interactions between non-Abelian anyons. With the pairwise anyon interactions typically showing RKKY-type oscillations in sign, but decaying exponentially with distance, we show that the character of the nucleated phase is fully determined by anyon interactions beyond nearest neighbor exchange. We investigate this issue in the context of Kitaev's honeycomb lattice model. In the presence of vortex lattices, depending on microscopic parameters such as the vortex lattice spacing, we observe the nucleation of several distinct Abelian topological phases, that differ in their band structure and Chern number description. By employing an effective model of Majorana fermions, we show that these phases can be fully predicted from the vortex-vortex interactions. Corresponding microscopic results should hold for vortices forming an Abrikosov lattice in a p-wave superconductor or quasiholes forming a Wigner crystal in non-Abelian quantum Hall states.

This talk focuses on an application of a WKB technique that is a generalization of the Born-Oppenheimer approximation to the Schwinger model of angular momentum. This work makes it possible to express the asymptotic limits of higher 3nj symbols in terms of the asymptotic limits of lower 3nj symbols, when only a subset of quantum numbers are taken to be large. After an introduction of the the technique, we show that the 15j symbol has different asymptotic limits in terms of a combination of several Ponzano Regge actions when different subsets of quantum numbers are taken large.

A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the Aharonov-Bohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the perspective of formulating the Spin Foam dynamics as the local interaction of topological defects.

Cosmology and quantum gravity have not always had the smoothest of interactions. As a case in point I'll summarize the calculation behind the prediction of tensor modes in inflationary universes and discuss the difficulties found in recasting this calculation in terms of Ashtekar-Barbero-Immirzi variables. Contrary to the belief that ``inflation is shielded from quantum gravity'', novelties are found, leading to the interesting prediction of a chiral signature in the gravitational wave background, proportional to the imaginary part of the Immirzi parameter. This would leave a distinctive imprint in the polarization of the cosmic microwave background. On a more theoretical level, our remarks shed light on matters permeating quantum gravity, such as the inner product, the ground state (which we prove is NOT the Kodama state) and ordering issues.

A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. Two fundamental challenges to any such approach are, at the conceptual level, the role of time in the emergent context and, technically, the fact that the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics and quantum field theory to the problem. We initiate a study of such problems using spin systems as toy models for emergent geometry and gravity. These are models of quantum networks with no a priori geometric notions. In this talk we present two models. The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This is essentially a Hubbard model on a dynamical lattice. We will see that regions of high connectivity behave like analogue black holes. Particles in their vicinity behave as if they are in a Schwarzchild geometry. Time permitting, I will show our study of the entanglement entropy of the system, which suggests particle localization near these traps.

A serious shortcoming of spinfoam loop gravity is the absence of matter. I present a minimal and surprisingly simple coupling of a chiral fermion field in the framework of spinfoam quantum gravity. This result resonates with similar ones in early canonical loop theory: the naive fermion hamiltonian was found to be just the extension of the simple

Emergent gravity scenarios have become increasingly popular in recent times. In this talk I will review some evidence in this sense and discuss some lessons from toy models based on condensed matter analogues of gravity. These lessons suggest some (possibly) general features of the emergent gravity framework which not only can be tested with current astrophysical observations but can also improve our understanding of cosmological puzzles such as the dark energy one. I shall review these tests and expectations and discuss the perspectives of this line of research and emergent gravity scenarios at large.