Phases of Quantum Field Theories: Symmetries and Vacua
FWF START project · Mathematical Physics, University of Vienna
Quantum field theory (QFT) is the fundamental framework of theoretical physics, used to describe a wide range of physical phenomena — from the smallest subatomic scales to the largest structures in the universe. Despite its many successes, much about QFT remains mysterious. To make progress, physicists often turn to a simplified version known as supersymmetric QFT, which allows us to study certain features of QFT in a more controlled setting, similar to conducting experiments in a laboratory.
Supersymmetric QFTs are characterised by their vacua (ground states) and symmetries. Vacua play a central role by determining the phase of the system and specifying which particles can exist. There are two key types of vacua: Higgs vacua and Coulomb vacua. Symmetries, in turn, dictate the rules governing the motion and interactions of these particles.
In my recent research, I have made some exciting discoveries that challenge our current understanding of Higgs vacua. Surprisingly, these vacua exhibit rich and unexpected quantum behaviours. To analyse these phenomena, I developed a specialised framework called magnetic quivers [1], inspired by the study of Coulomb vacua in three dimensions. Coulomb vacua are renowned for their intricate quantum effects, and recent breakthroughs have significantly advanced our understanding of them. Building on these insights, magnetic quivers provide a powerful algorithm and exact computational techniques for studying quantum Higgs vacua. Using this approach, we can determine the exact particle spectrum, identify the relevant symmetries, and map out phase diagrams.
Research Objectives
This project focuses on three main objectives:
1) Systematic analysis of quantum Higgs vacua
I aim to study quantum Higgs vacua across supersymmetric theories in dimensions ranging from three to six. These vacua are crucial for understanding the different phases of quantum field theories and provide a foundation for uncovering deep connections between theories in various dimensions.
2) Exploring quantum phenomena in three-dimensional Coulomb vacua
I continue to investigate the fascinating quantum effects emerging from three-dimensional Coulomb vacua, with a focus on their rich mathematical structures and the novel principles that govern their behaviour.
3) Discovering new quantum structures and defects
I am exploring innovative directions involving quantum defects and novel structures. In particular, I study how certain four-dimensional quantum field theories arise as defects inside six-dimensional theories, offering new perspectives on how different quantum systems interact and influence each other.
The outcomes of this project are expected to advance both physics and mathematics. In physics, the results provide unprecedented insights into quantum Higgs vacua across various dimensions. In mathematics, the methods developed offer fresh approaches to understanding the geometric structures underlying quantum field theories.
Milestones
1) Decay and Fission Algorithm
Magnetic quivers encode the quantum Higgs vacua of supersymmetric QFTs. These vacua are deeply connected to the celebrated Higgs mechanism: a chosen vacuum determines the masses of elementary particles and the strengths of fundamental forces. Different vacua can be grouped together according to similarities in the resulting physics, which gives the space of Higgs vacua an intricate internal structure.
Together with Antoine Bourget (Saclay, Paris) and Zhenghao Zhong (Oxford), I developed a simple and efficient algorithm to determine this structure directly from the magnetic quiver. A magnetic quiver can be represented using two objects: a vector K that encodes the vertices and a matrix A that specifies how the vertices are connected. A key result of our Physical Review Letters publication [2] is that while the matrix A remains fixed, the vector K can either (i) shrink (i.e. decay) or (ii) split — a process we call fission.
This concept successfully reproduces all known Higgs mechanisms of supersymmetric QFTs in dimensions three to six and has led to numerous new predictions.
For more information, please see the University of Vienna press release.
2) Extensions of the Decay and Fission Algorithm
We have extended the decay and fission algorithm to new classes of magnetic quivers [3,4]. Together with my PhD student Sinan [4], we have broadened the known set of unitary abelian magnetic quivers and classified the resulting Coulomb vacua.
3) Magnetic Quivers for New Classes of Supersymmetric QFTs
In [5], together with PhD student Lorenzo Mansi (DESY Hamburg), we demonstrated that magnetic quivers are powerful tools for studying little string theories — a remarkable class of six-dimensional supersymmetric theories with rich duality properties.
More recently, in collaboration with my postdoc Fabio [6], we showed that magnetic quivers can also describe the maximal branches of the moduli space of vacua in a broad class of three-dimensional Chern-Simons theories.
References
[1] S. Cabrera, A. Hanany, M. Sperling, “Magnetic quivers, Higgs branches, and 6d N=(1,0) theories”, JHEP 06 (2019) 071, JHEP 07 (2019) 137 (erratum), arXiv:1904.12293
[2] A. Bourget, M. Sperling, Z. Zhong, “Decay and Fission of Magnetic Quivers”, Phys. Rev. Lett. 132 (2024) 22, 221603, arXiv:2312.05304
[3] C. Lawrie, L. Mansi, M. Sperling, Z. Zhong, “A Pathway to Decay and Fission of Orthosymplectic Quiver Theories”, arXiv:2412.15202
[4] A. Bourget, Q. Lamouret, S. Moura Soysüren, M. Sperling, “Classification of Minimal Abelian Coulomb Branches”, arXiv:2412.19766
[5] F. Marino, M. Sperling, “Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories”, arXiv:2503.02744
"Phases of Quantum Field Theories: Symmetries and Vacua” (quiverQFT) is a research project awarded in the frame of the FWF-START program.
Grant-DOI: 10.55776/STA73
Duration: 01.10.2023 – 30.09.2028
