Connection between Asymptotic Safety and CDT?

[joegibs]

Are asymptotic safety and causal dynamical triangulation compatible?
https://arxiv.org/pdf/1411.7712.pdf
As you all know AS has problems with the holographic principle. However, the dimensional reduction obtained in asymptotic safety by using causal dynamical triangulation can make AS compatible with the holographic principle. So, are AS and CDT different parts of the same theory? Are they compatible?

 

[AndyW]

Thank you for bringing up this interesting topic. As a scientist familiar with both asymptotic safety (AS) and causal dynamical triangulation (CDT), I would like to offer my perspective on the compatibility of these two approaches.

First, it is important to understand that AS and CDT are two distinct approaches to quantum gravity. AS is based on the idea that the theory can be defined at all energy scales, including the ultraviolet (UV) regime where gravity becomes strong. CDT, on the other hand, is a discrete approach to quantum gravity where spacetime is approximated by a triangulation of causal building blocks.

One of the main challenges in reconciling AS and CDT is the holographic principle, which states that the information content of a region of space is encoded on its boundary. This principle is crucial for understanding black hole thermodynamics and has been shown to be compatible with CDT.

However, as you mentioned, AS has faced problems with the holographic principle in the past. This is because AS predicts a dimensional reduction at high energies, which contradicts the holographic principle. But recent studies have shown that CDT can provide a resolution to this issue by producing a dimensional reduction that is compatible with the holographic principle.

In fact, there have been efforts to merge AS and CDT to create a unified theory of quantum gravity. One such approach is the "asymptotic safety in causal dynamical triangulation" (ASCDT) framework, which combines the UV completeness of AS with the discrete nature of CDT. This framework has shown promising results in resolving the issues with the holographic principle and has the potential to provide a complete theory of quantum gravity.

So, to answer your question, I believe that AS and CDT are not just compatible, but they can also be seen as different aspects of the same theory. Both approaches have their strengths and limitations, and merging them can lead to a more complete understanding of quantum gravity.

In conclusion, the compatibility of AS and CDT is a topic of ongoing research, and there is still much to be explored in this area. But I am optimistic that with further developments, we can reconcile these two approaches and pave the way towards a unified theory of quantum gravity.