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arXiv · 2602.02082

On $E_{7+1/2}$ gauge theory

Xin Wang·Yi-Nan Wang
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Abstract

We study gauge theory based on the intermediate Lie algebra $E_{7+1/2}$, interpolating between $E_7$ and $E_8$. We propose a concrete UV completion via a 6d SCFT whose tensor branch description contains a pure $E_{7+1/2}$ gauge sector. The proposal is tested by 6d anomaly cancellation and by the 5d $\mathcal N=1$ Coulomb branch prepotential from the associated M-theory geometry. As a nonperturbative check, we determine the elliptic genus of the single-string worldsheet CFT using modular bootstrap. The result matches the vacuum character of the corresponding VOA for $E_{7+1/2}$, completing the elliptic genus/VOA correspondence along the Deligne-Cvitanovi\'{c} series.

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Xin Wang, Yi-Nan Wang. 2026-02-02. On $E_{7+1/2}$ gauge theory. https://arxiv.org/abs/2602.02082

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