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

Clay Cordova, Thomas T. Dumitrescu, Xi Yin

TL;DR

The paper analyzes the moduli-space effective actions of six-dimensional (2,0) SCFTs and their toroidal compactifications, using non-renormalization theorems to fix leading higher-derivative interactions from a one-loop five-dimensional YM analysis. It derives explicit formulas for the $a$-type Weyl anomaly and its monotonic decrease under $(2,0)$-preserving RG flows, and uses anomaly matching to support the ADE classification of (2,0) theories. By connecting tensor-branch dynamics to five- and four-dimensional theories, the authors provide a coherent, dimension-transcending picture of higher-derivative couplings, Wess-Zumino terms, and anomaly coefficients across dimensions. The results illuminate how ADE structure and SUSY constraints shape the IR/UV data and enable precise anomaly counts for all ADE (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.

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

TL;DR

The paper analyzes the moduli-space effective actions of six-dimensional (2,0) SCFTs and their toroidal compactifications, using non-renormalization theorems to fix leading higher-derivative interactions from a one-loop five-dimensional YM analysis. It derives explicit formulas for the -type Weyl anomaly and its monotonic decrease under -preserving RG flows, and uses anomaly matching to support the ADE classification of (2,0) theories. By connecting tensor-branch dynamics to five- and four-dimensional theories, the authors provide a coherent, dimension-transcending picture of higher-derivative couplings, Wess-Zumino terms, and anomaly coefficients across dimensions. The results illuminate how ADE structure and SUSY constraints shape the IR/UV data and enable precise anomaly counts for all ADE (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.

Paper Structure

This paper contains 26 sections, 107 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Review of $(2,0)$ Theories
  3. Anomalies
  4. Assumptions
  5. Summary of Results
  6. The Tensor Branch in Six Dimensions
  7. General Properties
  8. Non-Renormalization Theorems
  9. The Amplitude Point of View
  10. Compactification to Five Dimensions
  11. The Yang-Mills Description at the Origin
  12. Two-Derivative Terms and BPS States on the Coulomb Branch
  13. Four-Derivative Terms on the Coulomb Branch
  14. The Abelian Case
  15. Applications
  16. ...and 11 more sections

Figures (3)

  • Figure 1: Factorization of a six-point amplitude though a pair of $H^4$ vertices.
  • Figure 2: Factorization of a $7$-point amplitude though a pair of 4-derivative vertices.
  • Figure 3: One-loop box diagram in $d$ spacetime dimensions. The external lines are associated with the Cartan generator $t$ and the W-Bosons running in the loop correspond to a root $\alpha$.