CMSA Quantum Field Theory Program

Dates: August 30, 2027 – May 5, 2028

Location: Harvard CMSA, 20 Garden Street, Cambridge MA

Quantum field theory (QFT) has long been a subject with a large influence on mathematics, yet there is still no unified mathematical framework that encompasses all viewpoints.  Constructive QFT and Algebraic QFT—typified by the Wightman and Haag-Kastler axiom systems, respectively—have many achievements in relativistic and Euclidean QFT, but they do not include Wick-rotated theories on compact manifolds and so miss many of the geometric, topological, and algebraic developments of the past several decades.  These developments include supersymmetric QFT and applications to geometry and topology, generalized symmetries in QFT, and a robust theory of topological QFTs.  The more recent Segal and Costello-Gwilliam axiom systems do accommodate some of these developments, but they are largely disjoint from the analytic progress.  Techniques from probability theory and stochastic PDE have been used to advance traditional constructive and algebraic QFT; they have also been applied to obtain rigorous results in two-dimensional conformal field theory and Euclidean lattice gauge theories.  There has also been recent progress in quantum lattice systems, revealing surprising new bridges between operator algebras and topology.

This special year at CMSA aims to shape the direction of the field by bringing the analytic and geometric threads of mathematical QFT into closer contact.  The program will gather a diverse group of mathematicians together with physicists who enjoy close interactions with mathematicians.  The year will be organized around the four focus areas listed below.  There will be several short courses and one workshop for each of these focus areas.  All lectures will be hybrid.

FOCUS AREAS

First Semester

• Axiomatic approaches to QFT
• Symmetry, anomalies, and topology

Second Semester

• Probabilistic methods in QFT
• Supersymmetry, geometry, and moduli spaces

Organizers: 

• Sourav Chatterjee (Stanford University)
• Clay Cordova (University of Chicago)
• Dan Freed (Harvard University)
• Anton Kapustin (Caltech)
• Constantin Teleman (University of California, Berkeley)