Quantum Gravity

I argue that we do not understand gauge theory as well as we think when boundaries are present. I will briefly explain the conceptual and technical issues that arise at the boundary.  I will then propose a tentative resolution, which requires us to think of theories not in spacetime, but in field-space. 

Black holes are like bells; once perturbed they will relax through the emission of characteristic waves. The frequency spectrum of these waves is independent of the initial perturbation and, hence, can be thought of as a `fingerprint' of the black hole. Since the 1970s scientists have considered the possibility of using these characteristic modes of oscillation to identify astrophysical black holes. With the recent detection of gravitational waves, this idea has started to turn into reality.
Inspired by the black hole-fluid analogy, we demonstrate the universality of the black-hole relaxation process through the observation of characteristic modes emitted by a hydrodynamical vortex flow. The characteristic frequency spectrum is measured and agrees with theoretical predictions obtained using techniques developed for astrophysical black holes. Our findings allow for the first identification of a hydrodynamical vortex flow through its characteristic waves.
The flow velocities inferred from the observed spectrum agree with a direct flow measurement. Our approach establishes a non-invasive method, applicable to vortex flows in fluids and superfluids alike, to identify the wave-current interactions and hence the effective field theories describing such systems.

We present a consistent theory of classical gravity coupled to quantum field theory. The dynamics is linear in the density matrix, completely positive and trace-preserving, and reduces to Einstein's equations in the classical limit. Several no-go theorems are evaded since the assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally stochastic involving finite sized and probabilistic jumps in space-time and in the quantum field. Nonetheless the quantum state of the system can remain pure conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave-function. More generally, we derive a form of classical-quantum dynamics using a non-commuting divergence which has as its limit deterministic classical Hamiltonian evolution, and which doesn't suffer from the pathologies of the semi-classical theory. Details at http://arxiv.org/abs/1811.03116

The path integral approach to quantum gravity has given us many interesting results in the semiclassical regime. However, the canonical path integral for General Relativity still poses a variety of conceptual and computational challenges. To probe the deep quantum regime, Path Integral Monte Carlo (PIMC) techniques are being used successfully in approaches like Causal Dynamical Triangulations and Causal Set Theory. 

In this talk I will discuss how we can apply PIMC techniques to make the canonical Path Integral amenable to computation using matter-time. I will present results from PIMC simulations of homogeneous & isotropic cosmologies, and discuss the extension of this technique to anisotropic as well as inhomogeneous settings. 

I show that Unruh effect can be associated with the partitioning of the real line, and derived from the basic representation theory of the group of affine transformations in one dimension. This result shows that thermal distributions naturally emerge in connecting quantum
states belonging to representations related to distinct notions of translational symmetry.

I will present a new method to constrain the quantum effective action of gravity, inspired by recent results from causal dynamical triangulations (CDT). After a short introduction to CDT, I will start from a parameterisation of the effective action to calculate correlation functions for observable quantities. Matching these correlators to CDT data allows to reverse-engineer the couplings which describe the effective dynamics. As a concrete example, the autocorrelation of spatial volume fluctuations is considered. The comparison to CDT data suggests the existence of non-local interaction terms, which might have interesting phenomenological consequences for the interpretation of dark energy.

We consider a natural extension of general relativity, by the addition of a term which is a topological invariant when the cosmological constant is in fact constant.  Allowing the cosmological constant to vary, we discover it is endowed with a natural dynamics, which also includes a mechanism to suppress its value.   A key role in hiding the consequences of a dynamical cosmological constant is played by the torsion of the spacetime connection.

As a dynamical variable, the varying cosmological constant turns out to be canonically conjugate to a measure of intrinsic, cosmological time, given by the Chern-Simons invariant of the Ashtekar connection (which we originally studied with Chopin Soo).  As a result, a small quantum universe that "knows what time it is" does not know the value of the cosmological constant, and visa versa.   This leads to some novel scenarios for the early universe.

This is joint work in progress with Stephon Alexander, Joao Magueijo and Robert Sims.

As a proxy for a Quantum Gravity theory, String Theory introduces new degrees of freedom and symmetries that should play a major role in the physics of the early universe. We motivate the introduction of these ingredients as we review some of the issues of the inflationary paradigm. Among these new ingredients, T-duality may help us to solve the Big Bang singularity and yield a different cosmological scenario. Thus, we review how this has been thought in the context of Double Field Theory, which aims to build a covariant field theory under T-duality's group, and consider its cosmological applications. 

We  find an  approximation of  the induced spatial distance on a Cauchy hypersurface using only the causal structure and local volume element. The approximation can be made arbitrarily precise for a globally hyperbolic spacetime with compact Cauchy hypersurfaces. This prescription has a discrete analog which we use to evaluate the induced spatial distance in a continuum-like causal set.  As expected, because of  discrete asymptotic silence, this gives a poor approximation to the continuum distance in the "UV".  For larger distances, on the other hand, the approximation works very well, as long as the discreteness scale is significantly smaller than the extrinsic and intrinsic curvature scale of the spatial hypersurface. This paves the way for obtaining detailed spatial geometric information from the causal structure, which has implications for the continuum approximation of causal set theory. 

I discuss the canonical degrees of freedom of metric Einstein gravity on a null surface. The constraints are interpreted as conservation equations of a boundary current. Gravitational fluxes are identified, and the Hamiltonians of diffeomorphism symmetry are discussed. Special attention is given to the role of a modification of the phase space at the boundary of the null surface. Based on 1802.06135 with Laurent Freidel.

The large j asymptotic behavior of 4-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large j asymptotic behavior is determined by critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are phases asymptotically, whose exponents equal to Regge action of gravity. The amplitude also contains critical configurations corresponding to non-degenerate split signature 4-simplices and degenerate vector geometries.  

I will discuss certain irrelevant operator deformations of holographic conformal field theories that define a one parameter family of quantum field theories which are thought to be dual to quantum gravity in finite regions. 
Some examples include the "$T\bar{T}$ deformation of two dimensional holographic CFTs, its generalisations and higher dimensional cousins.
I will emphasise the key role played by emergent radial diffeomorphism invariance in this scenario. In particular, I will present an additional criterion for a theory, in the appropriate regime, to possess a dual description in terms of general relativity coupled to matter in one higher dimension. I will also discuss entanglement properties of such theories, and in a particular example, I will show how the holographic entanglement entropy conjectures still hold in the finite radius setting. This is based on the following work: arXiv:1707.08118 [hep-th], arXiv:1712.07955 [hep-th], arXiv:1806.07444 [hep-th] and arXiv:1808.07760 [hep-th]."