Phases of Quantum Field Theories: Symmetries and Vacua

Quantum field theory (QFT) is a framework used in theoretical physics to explain various physical phenomena, ranging from the smallest subatomic scales to the larger scales of our universe. While QFT has been successful in many ways, there is still much we do not understand about it. To address this, we rely on a simplified version called supersymmetric QFTs, which allows us to study specific aspects of QFT in a controlled manner, similar to a laboratory experiment.

Supersymmetric QFTs are characterised by their vacua (ground states) and symmetries. Vacua play a crucial role as they determine the phase of the system by defining what particles can exist. There are two types of vacua: Higgs and Coulomb. Symmetries, on the other hand, define the rules for motion and interaction of the particles.

In my recent research, I made some exciting discoveries that challenge our current understanding of Higgs vacua. Surprisingly, I found that Higgs vacua exhibit unexpected quantum behaviours. To analyse these phenomena, I developed a specialised program called "magnetic quivers," inspired by Coulomb vacua in three dimensions. Coulomb vacua are known for their challenging quantum effects, but recent breakthroughs have helped us make significant progress in understanding them. Building upon these insights, the magnetic quiver program provides a powerful algorithm and exact computational techniques to explore quantum Higgs vacua. Using this program, I can determine the exact spectrum (i.e. what particles exist), identify the symmetries involved, and even create phase diagrams.

This project has three main objectives. First, I aim to classify all the quantum Higgs vacua in six-dimensional supersymmetric QFTs, which hold a pivotal role in the realm of supersymmetric quantum field theories. This will lay the foundation for a systematic study of QFTs across different dimensions, not just in six space-time dimensions. Second, I will focus on the emerging three-dimensional Coulomb vacua and analyse the underlying mathematical structure of these new quantum vacua, which sheds light on the new rules governing the quantum behaviour. Lastly, by combining vacua, magnetic quivers, and defects, I will explore a novel direction: studying four-dimensional QFTs that can be realised as defects in six-dimensional supersymmetric QFTs. These defects, engineered based on knowledge of the Higgs vacua, support their own four-dimensional QFTs, which can be systematically analysed.

The outcomes of this project will advance both physics and mathematics. In physics, the results will provide unprecedented insights into the quantum Higgs vacua of QFTs in various dimensions. In mathematics, the intuitive QFT techniques offer a fresh perspective on the underlying geometric structures.

"Phases of Quantum Field Theories: Symmetries and Vacua” (quiverQFT) is a research project awarded in the frame of FWF-STAR­T program

You can read an interview with Marcus about his project HERE