From Field Theory to Geometry and Topology

Quantum field theory (QFT) and mathematical research are closely related to each other. QFT provides new tools for mathematics. A famous example of a connection of quantum field theory with topology is the three-dimensional Chern–Simons theory, whose Wilson loop correlators give the Witten–Reshetikhin–Turaev invariants of knots in 3-manifolds. Many other ideas from physics successfully made their way to mathematics including Feynman graphs and mirror symmetry. Conversely, many developments in geometry and topology have led to progress in QFT.


This fertile ground is one of the raisons d’être of the NCCR. Among the topics studied in this vast research direction are:


  • categorification
  • universal knot invariants
  • volume conjectures
  • applications to rational homotopy theory
  • homological methods in field theory
  • strings and enumerative problems
  • moduli spaces and cycles
  • representation theory and non-commutative geometry



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