Extended field theories and index theory
Lead Research Organisation:
Heriot-Watt University
Department Name: S of Mathematical and Computer Sciences
Abstract
An anomaly is the breaking of a classical symmetry under quantization. Following a proposal by D. Freed, a quantum field theory with anomaly can be described by a field theory relative to an extended field theory in one space-time dimension higher. All information about the anomaly is contained in this extended field theory.
The goal of this project is to study anomalies in condensed matter systems and string theory using extended field theories. This point of view allows the use of elaborate mathematical methods from (higher) category theory, gerbe theory and algebraic topology in this context. By using these methods we hope to produce new insights into the physics of the studied systems.
The goal of this project is to study anomalies in condensed matter systems and string theory using extended field theories. This point of view allows the use of elaborate mathematical methods from (higher) category theory, gerbe theory and algebraic topology in this context. By using these methods we hope to produce new insights into the physics of the studied systems.
Organisations
People |
ORCID iD |
Richard Joseph Szabo (Primary Supervisor) | |
Lukas Muller (Student) |
Publications
Müller L
(2020)
Equivariant higher Hochschild homology and topological field theories
in Homology, Homotopy and Applications
Müller L
(2019)
Parallel transport of higher flat gerbes as an extended homotopy quantum field theory
in Journal of Homotopy and Related Structures
Müller L
(2018)
A GNS construction of three-dimensional abelian Dijkgraaf-Witten theories
in Reviews in Mathematical Physics
Müller L
(2018)
Extended Quantum Field Theory, Index Theory, and the Parity Anomaly
in Communications in Mathematical Physics
Müller L
(2019)
't Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology
in Communications in Mathematical Physics
Bunk S
(2019)
Geometry and 2-Hilbert space for nonassociative magnetic translations
in Letters in Mathematical Physics
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
ST/N504099/1 | 30/09/2015 | 29/09/2020 | |||
1820602 | Studentship | ST/N504099/1 | 30/09/2016 | 30/03/2020 | Lukas Muller |