Fortschritte der Physik· 2015Q1
Atomic classification of 6D SCFTs
- 298citations
- Q1SCImago
- 2015year
Short summary
A novel classification of six-dimensional superconformal field theories (SCFTs) reveals that their tensor branches form linear chains of intersecting spheres with decorations at the ends.
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Key points
- Six-dimensional SCFTs are classified using F-theory by analyzing tensor branches and seven-brane configurations.
- Tensor branches are described as linear chains of intersecting spheres with end decorations, termed 'atoms', 'radicals', and 'molecules'.
- The resulting SCFT structures form generalized quivers with ADE-type nodes and conformal matter.
- A specific example involving E8 small instantons probing ADE singularities has an F-theory realization, matching mathematical group theory results.
AI-generated from the title and abstract; the full text is not read.
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 E8 small instantons probing an ADE singularity is shown to have an F-theory realization. This yields a classification of homomorphisms from ADE subgroups of into E8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis.
The authors' abstract, as published at the source. Fortschritte der Physik, 2015 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics