# Field Theory

Quantum field theory is the framework in which the force fields mediating elementary particle interactions are described. It is a basic ingredient in formulating the ideas of condensed matter physics, statistical mechanics and string theory, and has also given inspiration to a number of areas of mathematics including differential geometry, topology, non-commutative algebra, probability theory and combinatorics. Despite its ubiquity there remain many pressing unresolved issues particularly concerning the underlying mathematics.

The Field Theory project addresses questions in physics requiring sophisticated mathematical methods, and mathematical questions that can be solved by exploiting the wealth of ideas coming from physics.

**Specific projects include questions concerning:**

- Investigating quantum field theory in 3 and 4 dimensions using conformal bootstrap, renormalization group techniques, and cut-and-paste techniques.
- Studying holographic conformal field theory.
- Utilising homotopy theory, elliptic cohomology and low-dimensional topology, geometry of moduli spaces, Lie theory and representation theory to study quantum field theory.

### Project leader

Giovanni Felder

###### ETH Zurich

### Professors related to Field Theory

###### Anton Alekseev

###### Niklas Beisert

###### Anna Beliakova

###### Matthias Blau

###### Alberto Cattaneo

###### Ruth Durrer

###### Jean-Pierre Eckmann

###### Giovanni Felder

###### Jürg Fröhlich

###### Matthias Gaberdiel

###### Rinat Kashaev

###### Horst Knoerrer

###### Michele Maggiore

###### João Penedones

###### Tudor Ratiu

###### Riccardo Rattazzi

###### Amit Sever

###### Stanislav Smirnov

###### Alessandro Vichi

###### Thomas Willwacher

###### Peter Wittwer

###### Alexander Zhiboedov