A class of six-dimensional conformal field theories

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.

8 pages. More pedagogical presentation, added section on relationship to d = 4 Yang-Mills theory

References in corpus (4)

• Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence
• Weyl anomaly for Wilson surfaces
• Deformations of Chiral Two-Forms in Six Dimensions
• Holomorphic factorization of correlation functions in (4k+2)-dimensional (2k)-form gauge theory

Cited by in corpus (8)

• Structures on the Conformal Manifold in Six Dimensional Theories
• AdS_3 OM theory and the self-dual string or Membranes ending on the Five-brane
• M5/D4 brane partition function on a circle bundle
• Off-Shell N=2 Linear Multiplets in Five Dimensions
• On the Supersymmetric Index of the M-theory 5-brane and Little String Theory
• Superconformal Theories in Six Dimensions
• Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras
• BPS surface observables in six-dimensional (2,0) theory