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

Xin Wang, Yi-Nan Wang

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-Cvitanović series.

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

Abstract

We study gauge theory based on the intermediate Lie algebra , interpolating between and . We propose a concrete UV completion via a 6d SCFT whose tensor branch description contains a pure gauge sector. The proposal is tested by 6d anomaly cancellation and by the 5d 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 , completing the elliptic genus/VOA correspondence along the Deligne-Cvitanović series.
Paper Structure (4 sections, 63 equations, 1 figure, 2 tables)

This paper contains 4 sections, 63 equations, 1 figure, 2 tables.

Table of Contents

  1. Anomaly coefficients for $E_{7+1/2}$
  2. Partial resolution of the Weierstrass model on $\mathbb{F}_{10}$
  3. Prepotentials for 6d $E_{7+1/2}$ theories
  4. One-string elliptic genus for 6d $E_{7+1/2}$ SCFTs

Figures (1)

  • Figure 1: Three descriptions of a $(-10)$-curve in 6d F-theory with generic elliptic fibration over it: (a) $E_8$ gauge theory coupled to two copies of rank-1 E-string on a $(-10)$-curve; (b) Blow up $(-10)$-curve twice, to get $E_8$ gauge theory on a $(-12)$-curve; (c) $E_{7+1/2}$ gauge theory on a $(-10)$-curve.