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arXiv · 2611.03467

Fractional $θ$-dependence from the sum over all instanton sectors

Yui Hayashi·Mithat Ünsal
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Abstract

An instanton carries integer topological charge, seemingly at odds with the multibranched $θ$ dependence of the Yang-Mills vacuum. We show that summing over all instanton sectors resolves this mismatch in self-dual supersymmetric $\mathbb{C}P^{N-1}$ and $\mathrm{SU}(N)$ Yang-Mills theories with a chiral mass, in two and four dimensions. The path integral reduces to a sum of instanton moduli-space volumes, yielding the multibranched vacuum structure. In four dimensions, this extends Nekrasov's instanton counting for Seiberg-Witten theory to a QCD-like theory without scalars.

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Yui Hayashi, Mithat Ünsal. 2026-11-02. Fractional $θ$-dependence from the sum over all instanton sectors. https://arxiv.org/abs/2611.03467

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