Quantum Gravity

We discuss the minimal coupling of gauge fields to the dual graph lattice of Causal Dynamical Triangulations (CDT) as a preliminary step towards the investigation of more realistic systems of gravity coupled to bosonic and fermionic matter. We first introduce the CDT approach and how the gravity and gauge fields are discretized, for general dimensions and gauge groups, focusing on some of the algorithmic complications which arise. Next, we discuss some results from 2D simulations of CDT coupled to U(1) and SU(2) gauge groups, where we studied both gravity and gauge-related observables and the ones related to gauge fields, comparing them to analogous simulations in the flat case.

In this talk, I will explain the construction of a (1+1) spacetime with a wormhole and its conversion into a time-machine spacetime. Then, I will describe a massless scalar quantum field theory in such spacetime. I focus in comparing this quantization of the field in the time-machine spacetime with the quantization on the two-dimensional Einstein cylinder, the emergence of a zero mode and its regularization.

Zoom link:  https://pitp.zoom.us/j/94856731951?pwd=MnFNZjlkUHVVWkRRQTIxR0o0TDFnUT09

I will present an argument that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis. I will argue in particular that an apparent alternative to causal sets, viz. a certain sort of discrete Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way. For it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.

Zoom Link: https://pitp.zoom.us/j/96897602807?pwd=VkJ3VTAwYjhaTnJ3Z2ZVclZFYXErZz09

Cosmic inflation is an important paradigm of the early Universe which is so far developed in two equivalent ways, either by geometrical modification of Einstein's general relativity (GR) or by introducing new forms of matter beyond the standard model of particle physics. Starobinsky's R+R^2 inflation based on a geometric modification of GR is one of the most observationally favorable models of cosmic inflation based on a geometric modification of GR. In this talk, I will discuss in detail the fundamental motivations for Starobinsky inflation and present how certain logical steps in the view of its UV completion lead to the emergence of a gravity theory that is non-local in nature. Then I will establish how one can perform studies of the early Universe in the context of non-local gravity and what are the observational consequences in the scope of future CMB and gravitational waves. I will discuss in detail how non-local R^2-like inflation can be observationally distinguishable from the local effective field theories of inflation. 

We study D dimensional pure Einstein gravity theory in a region of spacetime bounded by a generic null boundary. We show besides the graviton modes propagating in the bulk, the system is described by boundary degrees of freedom labeled by D surface charges associated with nontrivial diffeomorphisms at the boundary. We establish that the system admits a natural thermodynamical description. Using standard surface charge analysis and covariant phase space method, we formulate  laws of null surface thermodynamics which are local equations over an arbitrary null surface. This thermodynamical system is generally an open system and can be closed only when there is no flux of gravitons through the null surface. Our analysis  extends the usual black hole thermodynamics to a universal feature of any area element on a generic null surface in a generic diffeomorphism invariant theory of gravity. 

Zoom Link: https://pitp.zoom.us/j/91590041045?pwd=UXpWY3JEd0QwK2hXanBzSkdPRC94UT09

In this talk, I will consider quantum effects on some specific black hole solutions and take into account their gravitational backreaction. In particular, I will describe the holographic construction of the quantum BTZ black hole (quBTZ) from an exact four-dimensional bulk solution.  I will present some of the thermodynamic properties of these black holes, focus on the generalized first law and analyze the different complexity proposals for the quBTZ. Our results indicate that Action Complexity fails to account for the additional quantum contributions and does not lead to the correct classical limit. On the other hand, the Volume Complexity admits a consistent quantum expansion and agrees with known limits.

We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

In this talk, I will revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isolated horizons. In particular, I will focus my attention on extremal black holes, for which the isometry algebra that preserves a sensible set of asymptotic boundary conditions at the horizon strictly includes the BMS algebra. The conserved charges that correspond to this BMS sector, however, reduce to those of superrotation, generating only two copies of Witt algebra. For more general horizon isometries, in contrast, the charge algebra does include both Witt and supertranslations, being similar to BMS but s.str. differing from it. I will also show how this is extended to the case of black holes in the Einstein-Yang-Mills case, where a loop algebra associated to the gauge group is found to emerge at the horizon.

A basic calculation in QFT is the construction of the Yukawa potential from a tree-level scattering amplitude. In the massless limit, this reproduces the 1/r potential. For gravity, scattering mediated by a massless graviton is thus consistent with the Newtonian potential.

In de Sitter spacetime, the cosmological constant gives rise to a mass-like term in the graviton propagator. This raises the question what the classical potential looks like when taking into account curvature effects.

In this talk, I will introduce an operator-based formalism to compute scattering amplitudes in curved spacetime, and I will show how to construct the Newtonian potential in a dS background. Remarkably, the potential gives rise to an additional repulsive force, and encodes the de Sitter horizon in a novel and non-trivial way.

Over the past decades, the asymptotic safety scenario has matured into a viable contender for a consistent theory of quantum gravity. However, the pressing question of unitarity is far from being settled. I will present important steps towards tackling this issue and show the first direct computation of the graviton spectral function in asymptotically safe quantum gravity with a novel Lorentzian renormalisation group approach. We find a positive graviton spectral function, showing a massless one-graviton peak and a multi-graviton continuum with an asymptotically safe scaling for large spectral values. For small spectral values, the effective field theory result is approached. I will indicate consequences for scattering amplitudes and unitarity.

We expect certain universal results in classical gravity to come unaltered from a quantum theory of gravity. In this talk, I will firstly discuss new ideas on this topic, and the latest understanding we have on this, in an accessible way. After that, I will focus on local symmetries in gravity, and obtain the most general off-shell algebra of diffeomorphisms that acts non-trivially at corners, where gauge charges are supported. Noether charges in Einstein gravity are then shown to generate a faithful representation of this algebra. After pausing and reviewing the covariant phase space formulation, explaining the questions and issues our community faced in successfully applying it to gravity, I will show how a careful treatment of embeddings allows us to establish a field space where Noether charges act canonically via Poisson bracket. This solves a longstanding puzzle in this field, opening doors to new promising investigations. I will conclude by mentioning them and commenting on how new proposals might shed light on old unanswered questions in quantum gravity.

Zoom Link: https://pitp.zoom.us/j/96552295909?pwd=cFZwcGxLdWlaWWhRS21RMExUd1RjQT09

I study the dynamics of a gyroscope far from an isolated source of gravitational waves. With respect to a local frame 'tied to the distant stars', the gyroscope precesses when gravitational waves cross its path, resulting in a net `orientation memory', carrying information on the gravitational wave profile. I show that the precession rate is given by the so-called "dual covariant mass aspect", providing a celestially local measurement protocol for this quantity. Moreover, I show that the net memory effect can be derived from the flux-balance equations for superrotation charges in the "generalized BMS" algebra. Finally, I show how the spin memory effect à la Pasterski et al. is reproduced as a special case.