N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$

Guido Festuccia; Jian Qiu; Jacob Winding; Maxim Zabzine

doi:10.1007/jhep03(2017)026

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arXiv · 1611.04868

N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$

Guido Festuccia·Jian Qiu·Jacob Winding·Maxim Zabzine

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Abstract

We construct 4D $\mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 \times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on $S^4$.

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Guido Festuccia, Jian Qiu, Jacob Winding, Maxim Zabzine. 2016-11-15. N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$. https://doi.org/10.1007/jhep03(2017)026

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