Branes, Gauge Theory and Gravity in Matrix Models

supported by the FWF
, P24713



Nature is governed by quantum mechanics. However, finding a consistent quantum theory which incorporates all fundamental interactions including gravity remains an elusive challenge in theoretical physics. The aim of this project is to develop further one of the most promising approaches towards this goal, based on matrix models of Yang-Mills type. These models incorporate gauge theory as well as (some form of) gravity on non-commutative or ``quantized'' space-time. The point is that the classical concept of a space-time continuum is replaced by a quantum notion of quantum space-time, which behaves as usual for large scales, but becomes “fuzzy” and non-classical at very short scales. Such a behaviour is expected on general grounds.


In recent years, there has been substantial progress in the understanding of the effective geometry and physics of these matrix models. The metric underlying gravity is not fundamental but emerges only effectively in the semi-classical low-energy limit. One specific model -- known as IKKT model -- is particularly well-suited for quantization. It is also closely related to string theory, but appears to evade some of the problems in conventional string theory. Its quantization can be carried out using well-known techniques from Yang-Mills gauge theory, which is a great simplification compared with general relativity.


In this project, the mathematical description and the physical implications of this matrix model will be investigated. One focus is on a novel type of “brane” solutions, which realize the idea of having compactified extra dimensions. This is very interesting both for gravity as well as for its relation to particle physics. The aim is to understand the resulting gravity theory, as well as the low-energy effective gauge theory and its relation with particle physics.


This project is a follow-up of a previous project.

A very simple sketch of the model can be found here.

For a more detailed exposition see here

Frequently asked questions about the physics involved



selected project-related publications and expositions: