The Weyl Anomaly from the 6D Superconformal Index

TL;DR

This paper establishes a method to derive the holographic Weyl anomaly coefficients in 6D (1,0) superconformal theories directly from the superconformal index, linking group theory invariants to anomaly corrections.

Contribution

It introduces differential operators that extract $ ext{O}(1)$ anomaly contributions from the large-$N$ superconformal index in six dimensions.

Findings

Derived explicit differential operators for anomaly extraction.

Linked anomaly corrections to superconformal representation invariants.

Enhanced understanding of holographic anomaly computations in 6D theories.

Abstract

We explore the connection between the holographic Weyl anomaly and the superconformal index in six-dimensional $(1,0)$ theories. Using earlier results from holographic computations of the $\mathcal O(1)$ contributions $\delta a$ and $\delta(c-a)$ to the corresponding six-dimensional Weyl anomaly coefficients, we derive a pair of differential operators that extracts these values from the large-$N$ single-trace index. In doing so, we also highlight the structure of these corrections in terms of group theory invariants of the superconformal representations.