Correlators of the Global Symmetry Currents of 4D and 6D Superconformal Theories

TL;DR

This paper investigates two-point correlators of $E_8$ global symmetry currents in 4D and 6D superconformal theories, revealing their high-energy behavior and implications for coupling to gauge theories, with derivations from multiple theoretical frameworks.

Contribution

It provides new calculations of correlators in superconformal theories and links high-energy behavior to gauge theory couplings, using field theory, M-theory, and F-theory approaches.

Findings

High-energy correlator behavior indicates coupling to $E_8$ gauge theories.

Three derivations of correlator expressions from different theoretical perspectives.

Coupling of 4D theories with multiple copies to $E_8$ gauge theory.

Abstract

We study the two-point correlators of the currents of the $E_8$ global symmetry in the $N=(1,0)$ superconformal six-dimensional theory as well as in the 4D superconformal theories upon toroidal compactification. From the high-energy behavior of the correlator we deduce that in 4D 10 copies of the superconformal theory with $E_8$ global symmetry can be coupled to an N=2 $E_8$ gauge theory. We present three alternative derivations for the expression for the correlators. One from field-theory, one from M-theory and one from F-theory.