6d, N=(1,0) Coulomb Branch Anomaly Matching

TL;DR

This paper introduces an anomaly matching mechanism for 6d N=(1,0) theories on their Coulomb branch, ensuring anomaly consistency via a Green-Schwarz-like cancellation involving integral quantization and charged strings.

Contribution

It proposes a novel anomaly matching framework for 6d N=(1,0) theories, extending Green-Schwarz anomaly cancellation to Coulomb branch scenarios with integral quantization conditions.

Findings

The anomaly mismatch must be a perfect square, ΔI8 = 1/2 X4^2.

X4 acts as an electric/magnetic source for tensor multiplets, producing charged strings.

The mechanism is verified for N=(2,0) theories and N=(1,0) SCFTs from E8 instantons.

Abstract

6d QFTs are constrained by the analog of 't Hooft anomaly matching: all anomalies for global symmetries and metric backgrounds are constants of RG flows, and for all vacua in moduli spaces. We discuss an anomaly matching mechanism for 6d N=(1,0) theories on their Coulomb branch. It is a global symmetry analog of Green-Schwarz-West-Sagnotti anomaly cancellation, and requires the apparent anomaly mismatch to be a perfect square, $\Delta I_8={1\over 2}X_4^2$. Then $\Delta I_8$ is cancelled by making $X_4$ an electric / magnetic source for the tensor multiplet, so background gauge field instantons yield charged strings. This requires the coefficients in $X_4$ to be integrally quantized. We illustrate this for N=(2,0) theories. We also consider the N=(1,0) SCFTs from N small $E_8$ instantons, verifying that the recent result for its anomaly polynomial fits with the anomaly matching mechanism.