Generalised global symmetries in 5d 𝒩=1 theories from the blow-up equations

@misc{harding2026generalised,
  title = {{Generalised global symmetries in 5d $\mathcalN=1$ theories from the blow-up equations}},
  author = {William Harding and Noppadol Mekareeya},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.06663},
  eprint = {2607.06663},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.06663},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Generalised global symmetries in 5d 𝒩=1 theories from the blow-up equations
AU  - William Harding
AU  - Noppadol Mekareeya
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2607.06663
UR  - https://arxiv.org/abs/2607.06663
AB  - Five-dimensional 𝒩=1 superconformal field theories admit a rich variety of generalised global symmetries, including higher-form and 2-group symmetries and their 'tHooft anomalies. We show that this data can be extracted directly from the blow-up equations governing the instanton partition functions of such theories on the Ω-background. The central object is the classical prefactor exp(−V_n) weighting each magnetic flux on the blown-up geometry: evaluated on a background for the electric 1-form symmetry, the fractional parts of its exponents encode the cubic self-anomaly of the 1-form symmetry and its mixed anomalies with the instanton, flavour, gravitational, and SU(2)_R symmetries. Combined with the faithful continuous global symmetry of the ultraviolet fixed point, determined from the superconformal index, the same data decides whether the theory possesses a 2-group symmetry or a mixed 'tHooft anomaly. We illustrate the method in gauge theories, including SU(4) and USp(4) with antisymmetric hypermultiplets and Spin(7) and Spin(8) with vector hypermultiplets, as well as in several families of non-Lagrangian theories. New results include the effective prepotentials of the B_N and B_N^(1,2,3) families, the cubic 1-form anomalies of the rank-two theories ℙ^2∪𝔽_3 and ℙ^2∪𝔽_6, and several mixed 1-form--flavour and 1-form--SU(2)_R anomalies.
ER  -