Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories

TL;DR

This paper investigates the effective action and Weyl anomalies of six-dimensional (2,0) superconformal theories, using compactification and one-loop calculations to establish the a-theorem and explore the ADE classification.

Contribution

It introduces a streamlined approach to non-renormalization theorems and computes the Weyl anomaly for all (2,0) theories, confirming the a-theorem in this context.

Findings

The a-type Weyl anomaly decreases along RG flows in (2,0) theories.

Leading higher-derivative operators are fixed by one-loop calculations.

The paper supports the ADE classification of (2,0) theories.

Abstract

We systematically analyze the effective action on the moduli space of (2,0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four dimensions. We present a streamlined approach to non-renormalization theorems that constrain this effective action. The first several orders in its derivative expansion are determined by a one-loop calculation in five-dimensional Yang-Mills theory. This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2,0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2,0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2,0) supersymmetry, thereby establishing the a-theorem for this class of theories. Along the way, we encounter various field-theoretic arguments for the ADE classification of (2,0) theories.