Quantum Gravity

Asymptotic safety offers a compelling UV completion of quantum gravity through a non-trivial UV fixed point. Evidence for this has so far come predominantly from the functional renormalization group. In this talk, I explore a complementary perturbative approach, which offers manifest gauge invariance and allows for computations directly in Lorentzian signature. A crucial ingredient for this is the use of renormalization schemes that are not mass-independent but retain sensitivity to power-law effects. Two realizations of this idea are discussed: a variant of dimensional regularization that goes beyond minimal subtraction, and an adaptation of gradient-flow techniques that have proven successful in QCD. As a proof of concept, I show that in QCD these ideas capture effects that would otherwise be missed, such as the decoupling of heavy quarks. Applying the same methods to gravity, I find that a UV fixed point already emerges at one-loop, with indications that it lies within a perturbative domain. I close by comparing these findings with functional renormalization group results on asymptotic safety and discussing future directions.

This talk is about the proposal that (1) quantum states that violate the momentum and Hamiltonian constraints represent instances of time, and (2) time evolution corresponds to the gradual collapse of an initial state toward a diffeomorphism-invariant state, driven by stochastic fluctuations of the lapse and shift. During the wavefunction collapse, the scale factor increases monotonically and thus acts as a clock. Scalar, vector, and tensor gravitons arise as physical excitations. In the long-time limit, the tensor gravitons exhibit emergent unitary dynamics, while the extra modes are damped by the non-unitary dynamics that suppress constraint-violating excitations. I will also comment on possible physical implications of these extra graviton modes.

In Einstein's theory of general relativity, the causal structure of spacetime is itself dynamical. Causality is encoded into the geometry of light cones that bend under the influence of gravity. Quantum theory, on the other hand, tells us that nature is intrinsically probabilistic. A sharply defined causal structure, as it appears in classical general relativity, contradicts quantum theory. A more general framework is needed. In this talk, I present a research programme in quantum gravity to develop a mathematical understanding of the causal structure at the quantum level. This is, in fact, a problem common to different approaches to quantum gravity, from holography, to the perturbative S-matrix approach and loop quantum gravity. After a brief introduction into the conceptual aspects of the problem, I will report on several new results on this frontier. First, I explain how to construct physical observables using the light cone geometry. Then, building upon earlier results in loop quantum gravity, we take the description to the quantum level. Finally, I explain how a fundamental quantum discreteness of geometry can alter the spectrum of highly luminous gravitational wave events. The talk is based on arXiv:2504.10802,2402.12578, 2401.17491, 2104.05803.

The classical action, or more generally the path integral, is a convenient framework for extracting the physical consequences of symmetries. In recent years, new symmetries of gravity in asymptotically flat spacetime have been uncovered based on relations to soft theorems governing the S-matrix. I will discuss a program to understand these symmetries using a formulation in which the S-matrix is identified with the action subject to asymptotic boundary conditions. This formulation of the S-matrix is analogous to the GKP/W formulation of the AdS/CFT duality and shares many of its advantages, albeit with new subtleties due to working in asymptotically flat spacetime.

A simple multiverse model explains the late time exponential expansion of our universe without the need of a cosmological constant. Assuming that the local measurement of H_0 is correct, it also give a better fit to data than the standard LCDM model, as well as a z-dependent state parameter w(z) that is not incompatible with the latest DESI data. An (tentative) underlying microscopic theory of the multiverse model, based on W_3 and exceptional Jordan algebras may allow us to calculate the expansion rate of our universe.