Emmy Noether Junior Research Group, Dr. Frank Saueressig

F. Saueressig, A. Contillo, O. Zanusso, S. Rechenberger M. Demmel

The four known fundamental forces of nature, i.e., the electromagnetic, weak, and strong interactions together with gravity, have a remarkably successful description in terms of the standard model of particle physics and general relativity, respectively. Notably, the two theories are on a very different theoretical footing, however: the standard model of particle physics is a quantum field theory (QFT) while general relativity constitutes a classical theory. Despite major efforts, constructing a quantum theory for gravity is still one of the prime challenges for theoretical high energy physics.

The main reason for this shortcoming is the fact that the perturbative quantization of general relativity results in a non-renormalizable QFT. Over the years this observation has led to many proposals for theories of Quantum Gravity which extend the framework of perturbative QFT in a more or less radical way. Some of the more prominent candidates are String Theory, Loop Quantum Gravity, lattice approaches as Regge calculus and Causal Dynamical Triangulations, or the Asymptotic Safety Program. The research activities of our group focus on various aspects of these theories.

Asymptotically Safe Quantum Gravity

The Asymptotic Safety Program is built on a rather mild generalization of perturbative QFT. Its essence is the conjecture that gravity constitutes a renormalizable and predictive QFT within Wilsons generalized framework of renormalization. In contrast to a perturbatively renormalizable QFT, where the continuum limit is taken at a Gaussian Fixed Point, the continuum limit of gravity is supposed to be governed by a non-Gaussian Fixed Point (NGFP) of the renormalization group flow. The primary tools for investigating this scenario are functional renormalization group equations. In recent years these have provided substantial evidence for the existence of this NGFP, mainly by studying truncations of the full flow equation. If this fixed point constitutes a genuine feature of the full theory, it provides a non-perturbative definition of Quantum Gravity, “Quantum Einstein Gravity” or “QEG” for short.

Our current research directions focus on

  • determining the number of relevant directions of the NGFP
  • investigating the stability of the NGFP under the inclusion of matter fields

A pedagogical introduction to the Asymptotic Safety Program can be found in the review article arXiv:0708.1317.

String Theory and Supergravity

A more radical avenue towards Quantum Gravity is pursued by String Theory. Here the framework of QFT is extended by assuming that the fundamental building blocks of the theory are one-dimensional oscillating lines, the strings. Besides gravity, the theory also contains all building blocks of the standard model (non-abelian gauge groups, bosons, fermions) and may thus unify all four fundamental forces. Its mathematical consistency furthermore requires additional ingredients as extra dimensions, supersymmetry, and additional extended objects, so-called branes.

In order to connect string theory to four-dimensional physics, it is typically assumed that the extra dimensions are given by a compact internal space. Below the typical length scale of the compact extra dimensions the physics can be captured by a four-dimensional low energy effective supergravity action, whose couplings are closely related to the geometric properties of the internal space.

In this context we work on

  • clarifying the geometric structures determining these supergravity actions
  • applying these structures in computing non-perturbative string corrections

This work is closely related to mathematical questions concerning the differential geometry of special holonomy manifolds and generalized mirror symmetry.