Path Integral Derivations of VafaWitten and KTheoretic Donaldson Invariants
[HYBRID WORKSHOP] New FourDimensional Gauge Theories October 24, 2022  October 28, 2022
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Supersymmetric gauge theory
topological quantum field theory
Donaldson invariants
Path Integral Derivations Of VafaWitten And KTheoretic Donaldson Invariants
I will discuss 5dimensional N=1 super YangMills compactified on X times S^1, with X a smooth, compact, oriented 4manifold. After a partial topological twist along X, the theory is locally independent of the metric on X, while it does depend on the radius R of S^1. The coefficients of the Rexpansion of the path integral correspond to the index of a Dirac operator on moduli spaces of instantons and monopoles, or more generally Ktheoretic Donaldson invariants. I will evaluate path integrals using two methods: 1) the quantum mechanics of the theory reduced to S^1 and 2) the low energy effective theory reduced to X. Both methods reproduce the same wallcrossing formula for 4manifolds with b_2^+=1. I will also discuss the evaluation of path integrals for 4manifolds with b_2^+>1 using method 2. Our results agree with those for algebraic surfaces by Gottsche, Nakajima and Yoshioka (2006) and Gottsche, Kool and Williams (2021). This talk is based on work in progress with H. Kim, G. Moore, R. Tao and X. Zhang.
Path Integral Derivations of VafaWitten and KTheoretic Donaldson Invariants

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Path Integral Derivations Of VafaWitten And KTheoretic Donaldson Invariants
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