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The Conformal Anomaly of M5-Branes

Travis Maxfield, Savdeep Sethi

TL;DR

The paper addresses the cubic growth of the conformal anomaly for the six-dimensional $(2,0)$ theory on N M5-branes by examining the Coulomb branch effective action. It develops a two-step approach: first relate the four-derivative couplings on $ ext{R}^{3,1} imes T^2$ to one-loop exact four-dimensional $ ext{N}=4$ SYM results, then deduce the six-derivative couplings from these data. Through detailed analysis of eight-fermion terms and their SUSY constraints in both 6d and 4d, and by matching torus compactifications, the authors show that the relevant four- and six-derivative couplings are controlled by a common constant, and that the six-dimensional anomaly scales as $N^3$ for rank-$N$ theories. The results provide a field-theoretic route to the $N^3$ growth, consistent with holographic expectations and anomaly inflow, and illuminate the structure of higher-derivative interactions in the $(2,0)$ theory.

Abstract

We show that the conformal anomaly for N M5-branes grows like $N^3$. The method we employ relates Coulomb branch interactions in six dimensions to interactions in four dimensions using supersymmetry. This leads to a relation between the six-dimensional conformal anomaly and the conformal anomaly of N=4 Yang-Mills. Along the way, we determine the structure of the four derivative interactions for the toroidally compactified (2,0) theory, while encountering interesting novelties in the structure of the six derivative interactions.

The Conformal Anomaly of M5-Branes

TL;DR

The paper addresses the cubic growth of the conformal anomaly for the six-dimensional theory on N M5-branes by examining the Coulomb branch effective action. It develops a two-step approach: first relate the four-derivative couplings on to one-loop exact four-dimensional SYM results, then deduce the six-derivative couplings from these data. Through detailed analysis of eight-fermion terms and their SUSY constraints in both 6d and 4d, and by matching torus compactifications, the authors show that the relevant four- and six-derivative couplings are controlled by a common constant, and that the six-dimensional anomaly scales as for rank- theories. The results provide a field-theoretic route to the growth, consistent with holographic expectations and anomaly inflow, and illuminate the structure of higher-derivative interactions in the theory.

Abstract

We show that the conformal anomaly for N M5-branes grows like . The method we employ relates Coulomb branch interactions in six dimensions to interactions in four dimensions using supersymmetry. This leads to a relation between the six-dimensional conformal anomaly and the conformal anomaly of N=4 Yang-Mills. Along the way, we determine the structure of the four derivative interactions for the toroidally compactified (2,0) theory, while encountering interesting novelties in the structure of the six derivative interactions.

Paper Structure

This paper contains 20 sections, 127 equations.

Table of Contents

  1. Introduction
  2. The basic idea and an outline
  3. SUSY Transformations and Conventions
  4. Effective actions and order counting
  5. $\mathcal{N}=4$ SYM in $d=4$
  6. $\mathcal{N} = (2,0)$ in $d = 6$
  7. $\mathcal{N} = (2,0)$ on $\mathbb{R}^{3,1}\times T^2$
  8. Eight Fermion Terms for Rank One
  9. $\mathcal{N} = (2,0)$ in $d=6$
  10. $\mathcal{N} = 4$ SYM in $d=4$
  11. $\mathcal{N}=(2,0)$ on $T^2$
  12. Zero-mode solutions
  13. Higher Fourier modes
  14. Determining the coefficients $c_n$
  15. Six Derivative Couplings in Six Dimensions
  16. ...and 5 more sections