Atomic classification of 6D SCFTs

By J. Heckman, D. Morrison, Tom Rudelius, C. Vafa. 2015

367 citations recorded by the source corpus.

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 SU(2) into E8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/593026f4ff4179468683cf2ee6b2b6337cc14b8f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Tom Rudelius
2. J. Heckman
3. Dan Xie
4. M. Del Zotto
5. C. Vafa
6. Yi-Nan Wang
7. Washington Taylor
8. D. S. Park

In Mathematical Physics

1. M. Del Zotto
2. C. Vafa
3. Tom Rudelius
4. Yi-Nan Wang
5. J. Heckman
6. Washington Taylor
7. Dan Xie
8. D. S. Park

In Nuclear and High Energy Physics

1. Washington Taylor
2. C. Vafa
3. Tom Rudelius
4. M. Del Zotto
5. Dan Xie
6. J. Heckman
7. Eran Palti
8. Yi-Nan Wang

Citations in the corpus

• On the Defect Group of a 6D SCFT (2015, background): “Recently, steady progress on the classification of such theories has been made [17–23], with a recently announced classification of theories (which is quite possibly complete) which can arise from compactifications of Ftheory [22].”
• Top down approach to 6D SCFTs (2018, background): “There are some exceptions to this generic behavior which are summarized in reference [125], but this is the essence of the structural classification of possible bases.”
• The F-theory geometry with most flux vacua (2015, methodology): “NonHiggsable clusters for base surfaces were classified in [13] and have provided a valuable tool in classifying elliptic threefolds and associated 6d supergravity theories [22, 23, 28–30] as well as 6d superconformal field theories [31–33].”
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2 (2015, methodology): “3.1 Orbifold 6d SCFTs 8 3.1.1 O(−n) models, i.e.”