2018/12/31 by Guido Festuccia, Jian Qiu, Jacob Winding +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Conjecture #Equivariant map #Field theory (psychology) #Fixed point #Geometric and Algebraic Topology #Geometry and complex manifolds #Instanton #Manifold (fluid mechanics) #Partition function (quantum field theory) #Topological quantum field theory #Vector field #hep-th #math.DG
paper · pdf · doi:10.1007/s00220-020-03681-9
published as Commun.Math.Phys. 377 (2020) 1, 341-385 · 58 pages, typos corrected, the final version to appear in CMP
openalex publication_date 2020/01/21 · openalex created_date 2020/01/30 · arxiv created 2020/03/31 · arxiv updated 2020/06/09 · openalex updated_date 2026/08/05
Abstract We construct N=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> supersymmetric Yang–Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equivariant Donaldson–Witten theory is a special case of our construction. We present a unified treatment of Pestun’s calculation on S4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>S</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> and equivariant Donaldson–Witten theory by generalizing the notion of self-duality on manifolds with a vector field. We conjecture the full partition function for a N=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> theory on any 4D manifold with a Killing vector. Using this new notion of self-duality to localize a supersymmetric theory is what we call “Pestunization”.