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

TL;DR

This paper introduces the intermediate Lie algebra $E_{7+1/2}$ gauge theory, proposing a UV completion via 6d SCFT, and verifies its consistency through anomaly cancellation, geometric analysis, and elliptic genus calculations.

Contribution

It presents the first concrete UV completion of the $E_{7+1/2}$ gauge theory using 6d SCFT and establishes the elliptic genus/VOA correspondence for this intermediate algebra.

Findings

Successful anomaly cancellation in 6d

Matching elliptic genus with VOA vacuum character

Validation of the $E_{7+1/2}$ gauge sector via geometric methods

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.