# Analytical Methods

Analytical results or even exact solutions, such as the solution of the Kepler problem, the Hydrogen atom or Onsager's solution of the 2D Ising model, to name just a few prominent examples, have contributed profoundly to the development of physics. Even though analytical methods are often developed for simplified/idealized setups, they can establish important paradigms, in particular in cases in which data from simulations are difficult to interpret as it often happens e.g. in strongly correlated systems. Furthermore, exact analytical solutions can provide interesting reference points from which more realistic systems may be studied with the help of perturbation theory.

Members of the WPC were heavily involved in some of the key modern developments in which analytical methods have lead to breakthroughs. In particular the Hamburg `Center for Mathematical Physics', Germany's largest center for modern mathematical physics, plays a leading role also for the foundations of the WPC.

The WPC activities in the pillar Analytical Methods comprise:

- Conformal Field Theory and Integrable Systems
- Duality Symmetries; AdS/CFT Correspondence
- Supersymmetric Gauge Field Theories
- Perturbation Theory and Integration in QFT
- String Theory and Geometry
- Algebra and Topology

Relevant groups are

Algebra, Topology, Lie Theory, Mathematical Physics (Department of Mathematics)

Prof. Dr. Ulf Kühn, Prof. Dr. Ingo Runkel, Prof. Dr. Tobias Dyckerhoff, Jun.-Prof. Dr. Julian Holstein, Jun.-Prof. Dr. Simon Lentner

Complex Geometry, Differential Geometry, Symplectic Geometry (Department of Mathematics)

NN, Prof. Dr. Vicente Cortés, Jun.-Prof. Dr. Klaus Kröncke, Prof. Dr. Jörg Teschner

Phenomenology and Methods of Quantum Field Theory (Deparment of Physics)

Prof. Dr. K Fredenhagen, Prof. Dr. B.Kniehl, Prof. Dr. S. Moch

Strings - String Theory and Supersymmetric Quantum Field Theories (Department of Physics)

Prof. Dr. Gleb Arutyunov, Prof. Dr. Jan Louis

String theory group (DESY)

Prof. Dr. Volker Schomerus, Prof. Dr. Jörg Teschner, Dr. Elli Pomoni, Dr. Pedro Liendo