Abstract
Computer simulations allow us to explore non-perturbative phenomena in physics. This has the potential to help us understand quantum gravity. Finding a theory of quantum gravity is a hard problem, but, in the last several decades, many promising and intriguing approaches that utilize or might benefit from using numerical methods were developed. These approaches are based on very different ideas and assumptions, yet they face the common challenge to derive predictions and compare them to data. In March 2018, we held a workshop at the Nordic Institute for Theoretical Physics (NORDITA) in Stockholm gathering experts in many different approaches to quantum gravity for a workshop on “Quantum gravity on the computer”. In this article, we try to encapsulate some of the discussions held and talks given during this workshop and combine them with our own thoughts on why and how numerical approaches will play an important role in pushing quantum gravity forward. The last section of the article is a road map providing an outlook of the field and some intentions and goalposts that were debated in the closing session of the workshop. We hope that it will help to build a strong numerical community reaching beyond single approaches to combine our efforts in the search for quantum gravity.
Highlights
Introduction to Various Approaches to QuantumGravityThroughout this article, we use different theories to exemplify the issues we want to discuss; as a reminder, let us give a quick overview over frequently mentioned theories and their salient aspects
Sometimes -called Euclidean dynamical triangulations to distinguish it from causal dynamical triangulations, these simplices are equilateral, with all edges having the same length
One possible relation discussed at the workshop, was to compare the 3-volume correlations computed in causal dynamical triangulations with an effective continuum theory
Summary
Throughout this article, we use different theories to exemplify the issues we want to discuss; as a reminder, let us give a quick overview over frequently mentioned theories and their salient aspects. The asymptotic safety approach [41] hinges on Weinberg’s idea [42] that quantum gravity, described as a quantum field theory, is non-perturbatively renormalizable, i.e., possesses an interacting fixed point of the renormalization group flow in the ultraviolet described by a finite amount of relevant coupling constants This hypothesis is investigated via the functional renormalization group [43], where one integrates out short scale degrees of freedom to derive an effective theory at larger scales. Bianca Dittrich described a thoroughly studied proposal in spin foam models based on the idea to relate theories by identifying the same physical transitions on different discretisations [47,48], and scales, in order to find theories giving consistent answers She emphasized that consistency is indispensable for extracting predictions from the theory, e.g., expectation values of observables. To make progress in this direction, it is worthwhile to implement approximations and simplifications in order to cover a larger part of the parameter space with given resources
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