About the workshop

It is often said that quantum gravity attempts to unify the two pillars of modern theoretical physics, general relativity and quantum theory. Very recently some quantum gravity researchers are realizing that a third pillar might be necessary in order to achieve the goal, namely statistical physics, or the theory of collective and critical phenomena, with the variety of insights it provides concerning exotic phases in condensed matter, new organizing principles and mathematical techniques.

Background independent approaches to quantum gravity, such as Loop Quantum Gravity, Spin Foams and Group Field Theories, quantum Regge calculus and Dynamical Triangulations, Asymptotic Safety, emerged as serious candidates. Background independence means that these theories do not start by assuming the existence of a given smooth background spacetime: such a spacetime has rather to emerge dynamically out of the fundamental structures of the theory. As such, their fundamental dynamics has necessarily to depart drastically from that of General Relativity. Moreover, most of these background independent approaches are based on discrete structures (e.g. spin networks in loop quantum gravity, simplices in dynamical triangulations, both of them in group field theories), so that a smooth spacetime manifold, which also reflects the large scale dynamics of general relativity, has to emerge from fundamental discreteness in some kind of continuum or low energy limit. To show how this is realized is actually the most pressing open problem for all these approaches. It is also the main focus of our workshop.

On top of achieving important results, the mentioned quantum gravity approaches have somewhat converged towards each other, with simplicial complexes and discrete gravity actions, the main ingredients of quantum Regge calculus and Dynamical Triangulations, acquiring a central role in the construction of spin foam models, for the description of the quantum dynamics of spin networks, the quantum states of geometry identified by loop quantum gravity. The stage is therefore set for joining forces, merging respective insights and results, and tackling together their common open issues. This explains why the proposed workshop brings together experts on several quantum gravity approaches, and especially young researchers, to work jointly on the problem of the continuum.

This common problem takes of course different aspects depending on the specific formalism used. For example, spin foam models and simplicial quantum gravity approaches are formulated in terms of lattice discretization of gravity; the continuum approximation requires some background independent generalization of the coarse graining or refinement procedure of the spacetime lattice, of the type used in discrete statistical systems. In group field theory, on the other hand, spin networks and simplices are the fundamental quanta of a non-local field theory which encodes their collective dynamics. The type of GFT configuration needed in order to admit a continuum approximation is one constituted by a large number of GFT quanta, and therefore statistical (group) field theory is then the natural language to study the corresponding physics. In both settings, spacetime becomes akin to a (very) exotic condensed matter system, made out of many fundamental “atoms of quantum space”, and the discrete-continuum transition is then naturally seen as a phase transition following from their collective dynamics. It is therefore crucial for researchers in quantum gravity, who want to address the problem of the continuum, to master and be well-acquainted with techniques and results obtained in statistical physics, and to collaborate directly with experts in this area; conversely, statistical field theorists, experts in renormalization group techniques, phase transitions or lattice systems, with an interest in spacetime physics, find now several well-developed approaches to quantum gravity to which their expertise and language can be directly applied. This workshop will be a further step in establishing a common interdisciplinary framework, for quantum gravity researchers and statistical physicists, for the study of the discrete/continuum transition of quantum spacetime.