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Anomaly polynomial of general 6d SCFTs

Kantaro Ohmori, Hiroyuki Shimizu, Yuji Tachikawa, Kazuya Yonekura

Abstract

We describe a method to determine the anomaly polynomials of general 6d $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,0)$ SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. We demonstrate our method in many concrete examples, including $\mathcal{N}=(2,0)$ theories of arbitrary type and the theories on M5 branes on ALE singularities, reproducing the $N^3$ behavior. We check the results against the anomaly polynomials computed M-theoretically via the anomaly inflow.

Anomaly polynomial of general 6d SCFTs

Abstract

We describe a method to determine the anomaly polynomials of general 6d and SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. We demonstrate our method in many concrete examples, including theories of arbitrary type and the theories on M5 branes on ALE singularities, reproducing the behavior. We check the results against the anomaly polynomials computed M-theoretically via the anomaly inflow.

Paper Structure

This paper contains 32 sections, 104 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Without 6d gauge group
  3. With 6d gauge group
  4. Rank-1 examples
  5. $Q$ M5-branes on $\mathbb{C}^2/\mathbb{Z}_k$
  6. Organization of the paper
  7. Tensor branches without gauge multiplets
  8. Generalities of self-dual tensor fields in 6d
  9. 6d Green-Schwarz and 5d Chern-Simons
  10. $\mathcal{N}{=}(2,0)$ theories
  11. E-string theory of arbitrary rank
  12. Tensor branches with gauge multiplets
  13. Basic ideas
  14. A consistency condition on the theory
  15. M5 branes on ALE singularities
  16. ...and 17 more sections