On the classification of 6D SCFTs and generalized ADE orbifolds

By J. Heckman, D. Morrison, C. Vafa. 2013

375 citations recorded by the source corpus.

A bstractWe study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity ℂ2/Γ with Γ a discrete subgroup of U(2). When Γ is a subgroup of SU (2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2, 0) SCFTs. For more general U(2) subgroups, the allowed possibilities for Γ are not arbitrary and are given by certain generalizations of the A- and D-series. These theories should be viewed as the minimal 6D SCFTs. We obtain all other SCFTs by bringing in a number of E-string theories and/or decorating curves in the base by non-minimal gauge algebras. In this way we obtain a vast number of new 6D SCFTs, and we conjecture that our construction provides a full list.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1f47b13e2987e3a7179e51c4d8fc8dee47484e45

How researchers see this paper

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

In Mathematical Physics

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

In Nuclear and High Energy Physics

1. C. Vafa
2. Tom Rudelius
3. Dan Xie
4. J. Heckman
5. D. Gaiotto
6. M. Del Zotto
7. Washington Taylor
8. D. Morrison

In Statistical and Nonlinear Physics

1. Dan Xie
2. Tom Rudelius
3. J. Heckman
4. M. Del Zotto
5. C. Vafa
6. Washington Taylor
7. D. Gaiotto
8. Yuji Tachikawa

Citations in the corpus

• Anomaly polynomial of general 6D SCFTs (2014, methodology): “We end the section by re-phrasing our results in terms of the F-theory geometry, used in the classification in [12].”
• F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “for the construction of semi-realistic GUTs in global F-theory compactifications starting with [10,11] or the classification and study of 6D SCFTs [12–14].”
• On the Defect Group of a 6D SCFT (2015, background): “One of the results of reference [17] is that there is a generalized ADE classification of (1, 0) theories.”
• Holography for (1,0) theories in six dimensions (2014, background): “In F-theory, which goes beyond IIB supergravity, [7] recently found many (1, 0) theories, and classified them.”
• N=1 theories of class S_k (2015, background): “There is a rather large number of known (1, 0) SCFTs, many of which can be built through F-theory constructions [20, 21].”
• 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.”
• 6d Conformal matter (2014, methodology): “Recent work [12] gave a complete classification of (1, 0) theories without a Higgs branch.”
• 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].”
• Top down approach to 6D SCFTs (2018, methodology): “Another interesting feature of the above local model is that for special values of n and tuned values of the complex structure moduli, we can present the entire construction as an orbifold of the form [39,120]: ( C × T 2 ) /Γ.”
• Atomic classification of 6D SCFTs (2015, methodology): “As explained in [20], for a 6D SCFT, each such base consists of a connected configuration of curves built from (a) ADE configurations of −2 curves, and (b) configurations of curves known as “non-Higgsable clusters” [21], possibly joined by curves of self-intersection −1.”