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Fractional θ-dependence from the sum over all instanton sectors
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 ℂPN−1 and 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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BibTeX
@misc{hayashi2026fractional,
title = {{Fractional $θ$-dependence from the sum over all instanton sectors}},
author = {Yui Hayashi and Mithat Ünsal},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03467},
eprint = {2611.03467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03467},
}
RIS
TY - UNPB
TI - Fractional θ-dependence from the sum over all instanton sectors
AU - Yui Hayashi
AU - Mithat Ünsal
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03467
UR - https://arxiv.org/abs/2611.03467
AB - 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 ℂP^N−1 and 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.
ER -