Generalized Symmetries in Quantum Field Theory and Holography

The goal of this project is the comprehensive analysis of higher form symmetries in quantum field theories in various dimensions. Higher form symmetries generalize the concept of `ordinary' symmetries studied widely in quantum field theory, and mathematical physics more broadly. Ordinary symmetries have charged objects given by local operators and charge operators that are topological of codimension one. This concept can be extended to higher dimensional charged objects to describe a higher form symmetry. Many standard results carry over to this generalization, but the broader scope also allows for new physical insights to be obtained by studying the higher form symmetries of a theory.

A particular focus will be on conformally invariant theories with supersymmetry. These will be studied starting with the 6d superconformal theories (SCFTs), which upon dimensional reduction and RG-flow give rise to lower dimensional SCFTs. The project will focus on studying the relation between higher form symmetries and the dimensional reduction, in particular from 6d to 5d/4d/3d. Furthermore, the study of higher form symmetries will also require the analysis of 't Hooft anomalies of such global symmetries, as well as mixed anomalies between higher form symmetries.

To complement this field theoretic approach, the project will also analyze the imprint of higher form symmetries in the holographic dual descriptions of SCFTs. Holography has emerged as a framework for studying strongly-coupled SCFTs, in terms of a dual gravitational theory in an anti-de Sitter (AdS) spacetime. The dual SCFT lives at the boundary of the AdS spacetime, and properties such as symmetries of the SCFT are captured in terms of the gravity solution (both in the geometry as well as the fluxes). This part of the project will explore the manifestation of the different global choices of gauge groups and other higher form symmetry structures in the context of these holographic dualities. The key advantage to this framework is that it allows us to study such symmetries in the strong coupling regime of quantum field theories.

The methodology will draw from a variety of areas of mathematical physics: perturbative quantum field theory methods, geometric engineering, as well as holographic dualities. This utilizes both insights from physics as well as mathematics, in particular geometry and topology. Surprisingly, given their fundamental nature, higher form symmetries have a relatively short history dating back to the seminal paper in 2014, by Gaiotto, Kapustin, Seiberg and Willett. The analysis of generalized symmetries in higher dimensions has in fact only been initiated recently, and is a very active and exciting field of research.


This project falls within the EPSRC Mathematical Physics research area.