The anomaly field theories of six-dimensional (2,0) superconformal theories
Samuel Monnier
TL;DR
The paper constructs 7D anomaly field theories that encode the gravitational and R-symmetry anomalies of 6D $(2,0)$ SCFTs and explains how conformal blocks arise from this framework, with the anomaly theory defined on \'$(2,0)$-manifolds\' carrying a rank-5 R-symmetry bundle. The construction factorizes into invertible pieces (via half- and quarter-Dai-Freed theories, Hopkins-Singer theory, and BF/Chern-Simons terms) and a non-invertible discretely gauged Wu Chern-Simons sector, the latter being responsible for the nontrivial conformal-block structure. The main results provide explicit formulas for the anomaly field theories of ADE $(2,0)$ SCFTs, including detailed Hopf-Wess-Zumino contributions and their dependence on Wu structures, while also outlining the data required to define $(2,0)$-theories on topologically nontrivial spacetimes. The work connects M-theory inflow to higher-dimensional anomaly theories, clarifies the dimension of the conformal-block space as $|H^3(M;oldsymbol{ m Λ}_{ rak g}^*/oldsymbol{ m Λ}_{ rak g})|^{1/2}$ (up to torsion subtleties), and offers a structured framework for incorporating defects and extending to general ADE algebras. Overall, this provides a rigorous topological and geometric foundation for understanding global anomalies and conformal blocks in the elusive $(2,0)$ SCFTs, with potential implications for dualities and lower-dimensional compactifications.
Abstract
We construct 7-dimensional quantum field theories encoding the anomalies of conformal field theories with (2,0) supersymmetry in six dimensions. We explain how the conformal blocks of the (2,0) theories arise in this context. A result of independent interest is a detailed specification of the data required to define a (2,0) theory with topologically non-trivial spacetime and R-symmetry bundle.