Four-dimensional N=2 Field Theory and Physical Mathematics

2012/11/10 by Gregory W. Moore, Moore, Gregory W.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1211.2331

openalex publication_date 2012/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a summary of a talk delivered at the 2012 International Congress on Mathematical Physics. We review d=4, N=2 quantum field theory and some of the exact statements which can be made about it. We discuss the wall-crossing phenomenon. An interesting application is a new construction of hyperkahler metrics on certain manifolds. Then we discuss geometric constructions which lead to exact results on the BPS spectra for some d=4, N=2 field theories and on expectation values of -- for example -- Wilson line operators. These new constructions have interesting relations to a number of other areas of physical mathematics.

Citations

• N=2 Quantum Field Theories and Their BPS Quivers
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

Related

• Non-Perturbative Field Theory - From two dimensional conformal field theory to QCD in four dimensions
• Complex structure and the construction of the :ϕ⁴₄: quantum field theory in four-dimensional space-time
• Families of N=2 field theories
• On the Road Towards the Quantum Geometer's Universe: An Introduction to Four-Dimensional Supersymmetric Quantum Field Theories
• Topological quantum field theory and four-manifolds