Classifying bases for 6D F-theory models

By D. Morrison, Washington Taylor. 2012

268 citations recorded by the source corpus.

We classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors (“clusters”) that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f4, e6, e8, e8, (g2 ⊕ su(2)); and su(2) ⊕ so(7) ⊕ su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a5bc2ffa175e94a3e264f4394c644c7e4928989d

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Citations in the corpus

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): “The key observation of reference [108] is that in this maximally Higgsed phase, we can characterize the geometry of the base in terms of a configuration of minimal building blocks.”
Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2 (2015, background): “These models are very interesting as these are among the simplest 6D (1,0) tensor-vector systems which have a single tensor and are non-Higgsable as well [45, 50].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “The first group of approaches focuses on the classification and construction of all bases B that are admissible for F-theory [28–30].”
On the Defect Group of a 6D SCFT (2015, background): “The building blocks for these bases involve the so-called non-Higgsable clusters (NHCs) of reference [55], which include the important observation that there is a minimal canonical singular fiber type associated with each such cluster.”
On the classification of 6D SCFTs and generalized ADE orbifolds (2013, methodology): “, after activating all possible hypermultiplet vevs, it is possible to classify the resulting models in terms of the geometry of the base B [21].”
6d Conformal matter (2014, background): “These NHCs have been determined in [27], and consist of a configuration of up to three curves.”
Atomic classification of 6D SCFTs (2015, methodology): “4 spn fibers and enhancement of g2 factors It was pointed out in [21] that the mixed representation of the g2 ⊕ su2 gauge algebra may at times enhance from 1 2 (7,2) to 1 2 (7+1,2).”