Wormhole Renormalization: The gravitational path integral, holography, and a gauge group for topology change

Euclidean wormholes -- geometries which connect disconnected boundaries -- present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies...

In this thesis we study two different approaches to holography, and comment on the possible relation between them. The first approach is an analysis of the high-energy regime of quantum gravity in the eikonal approximation, where the theory reduces to a topological field theory. This is the regime where particles interact at high energies but with small momentum transfer. We do this for the cases of asymptotically dS and AdS geometries and find that in both cases the theory i...

We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology and natural sciences and creates a new platform for exploring geometrical physics.

Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field theories (qfts) by means of path integrals. This article uses their results to study whether qfts can be made compatible with topology changes. We show that path integrals over metrics need a finite norm for the latter and for degenerate me...

This is the written version of a lecture given at the ``VI Mexican School of Gravitation and Mathematical Physics" (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature on the subject. This account is geared towards graduate studen...

The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a ...

For two-dimensional holographic CFTs, we demonstrate the role of Berry phases for relating the non-factorization of the Hilbert space to the presence of wormholes. The wormholes are characterized by a non-exact symplectic form that gives rise to the Berry phase. For wormholes connecting two spacelike regions in gravitational spacetimes, we find that the non-exactness is linked to a variable appearing in the phase space of the boundary CFT. This variable corresponds to a loop ...

A remarkable result at the intersection of number theory and group theory states that the order of a finite group $G$ (denoted $|G|$) is divisible by the dimension $d_R$ of any irreducible complex representation of $G$. We show that the integer ratios ${ |G|^2 / d_R^2 } $ are combinatorially constructible using finite algorithms which take as input the amplitudes of combinatoric topological strings ($G$-CTST) of finite groups based on 2D Dijkgraaf-Witten topological field the...

This is my Th\`ese d'Habilitation (HDR) on the topic of spinfoam models for quantum gravity, which I presented in l'Ecole Normale Sup\'erieure de Lyon on december 16 2010. The spinfoam framework is a proposal for a regularized path integral for quantum gravity, inspired from Topological Quantum Field Theory (TQFT) and state-sum models. It can also be seen as defining transition amplitudes for the quantum states of geometry for Loop Quantum Gravity (LQG).

It is well-known that perturbative quantum gravity is non-renormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this essay, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitati...