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Master Topics for winter term 2025/2026Click on the topic titles below to see more details, or watch the video. The slides of that presentation can be found here. In order to discuss the topics in more detail, come to my office 28A 414 on Friday, 04 July 2025, 11:30h. To apply, follow the instructions here, where you can also find topics from the other members of our institute. Gradient FlowThe gradient flow is a concept which provides a bridge between perturbative and non-perturbative physics. The crucial parameter switching between these two regimes is the flow time t. Examples for projects:Flavor physicsThe lifetime and mixing parameters of bound quark states is a prime example for the application of the gradient flow. In this project, you will provide important input to the determination of these parameters. You will learn the concepts of the gradient flow, effective field theories, flavor physics, and perturbative calculations. We are working in close cooperation with lattice experts on this topic, so you will also get insight into this field. Related publications from our group:
Gradient flow in gravity = Ricci flowApplying the concept of the gradient flow to gravity leads to the so-called Ricci flow. It is a well-known concept in topology and was used by Grigori Perelman to prove the Poincaré conjecture. In this project, you are going to consider the Ricci flow from a perturbative perspective. This corresponds to a novel regularization of the UV divergences in gravity and may lead to new insights concerning its renormalization group structure.
The flowed QED beta function at four loopsOne of the most promising applications of the gradient flow is to derive the strong coupling from first principles. Our group has provided the required three-loop input for this a few years ago. The accuracy of the strong coupling derived from this analysis is of the order of the current world average. It could be significantly improved by going to four loops. In this project, you would provide the first step in this direction by considering the much simpler case of the QED coupling, which, by the way, even has its own applications when studying the structure of fixed points in gauge theories. You would do the first four-loop calculation in the gradient flow.
Effective Field TheoriesEffective Field Theories describe physics beyond the Standard Model in a generic way. Their construction is algorithmic, but very cumbersome. In the past, we have developed the program AutoEFT that generates an effective field theory for general chiral fields. Examples for projects:Flavor structuresThe Effective Field Theory based on the Standard Model (SMEFT) suffers from a large number of parameters. In order to determine them from experiment, one typically needs to make assumptions on the flavor structure of the UV theory. Examples are Minimal Flavor Violation, or the Froggatt-Nielsen model. In this project, you will study such structures systematically with the help of AutoEFT. You will learn the concepts of Effective Field Theories, flavor physics, and group theory. Related publications from our group:
A Rosetta stone for Effective Field TheoriesThe representation of an Effective Field Theory is not unique. In order to be able to compare experimental results to theoretical predictions, it is necessary to be able to translate one operator basis into the other. In this project, you will work out a conversion method for operator bases and supply AutoEFT with the capability to express arbitrary operators in terms of a particular basis. You will learn the concepts of effective field theories and group theory. Related publications from our group:
last updated on Jul 03, 2025 by RH
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