Atomic classification of 6D SCFTs. Issue 7 (11th June 2015)

• Record Type: Journal Article
• Authors: Heckman, Jonathan J.; Morrison, David R.; Rudelius, Tom; Vafa, Cumrun
• Is Part Of: Fortschritte der Physik. Volume 63:Issue 7/8(2015:Jul.)
• Page Start: 468
• Page End: 530
• Publication Date: 2015-06-11
• Subjects: Physics -- Periodicals; 530.05
• DOI: 10.1002/prop.201500024
• Languages: English
• ISSNs: 0015-8208

Abstract

Abstract : We use F‐theory to classify possibly all six‐dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F‐theory (which correspond to allowed collections of contractible spheres) and then classify all possible configurations of seven‐branes wrapped over them. We describe the first step in terms of "atoms" joined into "radicals" and "molecules, " using an analogy from chemistry. The second step has an interpretation via quiver‐type gauge theories constrained by anomaly cancellation. A very surprising outcome of our analysis is that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends. The resulting structure of these SCFTs takes the form of a generalized quiver consisting of ADE‐type nodes joined by conformal matter. A collection of highly non‐trivial examples involving E 8 small instantons probing an ADE singularity is shown to have an F‐theory realization. This yields a classification of homomorphisms from ADE subgroups of S U ( 2 ) into E 8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis. Abstract : We use F‐theory to classify possibly all six‐dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F‐theory (which correspond to allowed collections of contractible spheres) and then classify all possible configurations of seven‐branes wrapped over them. We describe the first step in terms of "atoms" joined into "radicals" and "molecules, " using an analogy from chemistry. The second step has an interpretation via quiver‐type gauge theories constrained by anomaly cancellation. A very surprising outcome of our analysis is that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends. The resulting structure of these SCFTs takes the form of a generalized quiver consisting of ADE‐type nodes joined by conformal matter. A collection of highly non‐trivial examples involving E 8 small instantons probing an ADE singularity is shown to have an F‐theory realization. This yields a classification of homomorphisms from ADE subgroups of S U ( 2 ) into E 8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis.