A class of six-dimensional conformal field theories

TL;DR

This paper introduces a new class of six-dimensional conformal field theories with properties similar to tensionless string theories, including an $ADE$-classification and S-duality behavior, extending the understanding of M-theory five-brane dynamics.

Contribution

It proposes a novel class of 6D conformal field theories related to tensionless strings, with specific algebraic and duality properties, and connects them to M-theory five-brane world-volume theories.

Findings

Theories exhibit $ADE$-classification and no extra parameters.

Hilbert space representation matches tensionless string theories.

Compactification reproduces S-duality behavior of super Yang-Mills.

Abstract

We describe a class of six-dimensional conformal field theories that have some properties in common with and possibly are related to a subsector of the tensionless string theories. The latter theories can for example give rise to four-dimensional $N = 4$ superconformal Yang-Mills theories upon compactification on a two-torus. Just like the tensionless string theories, our theories have an $ADE$-classification, but no other discrete or continuous parameters. The Hilbert space carries an irreducible representation of the same Heisenberg group that appears in the tensionless string theories, and the `Wilson surface' observables obey the same superselection rules. When compactified on a two-torus, they have the same behaviour under $S$-duality as super Yang-Mills theory. Our theories are natural generalizations of the two-form with self-dual field strength that is part of the world-volume theory of a single five-brane in $M$-theory, and the $A_{N - 1}$ theory can in fact be seen as arising from $N$ non-interacting chiral two-forms by factoring out the collective `center of mass' degrees of freedom.