2018/01/31 by Patrick Jefferson, Sheldon Katz, Hee-Cheol Kim +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.AG
paper · pdf · doi:10.1007/jhep04(2018)103
66 pages + appendices. v3: Comment added concerning a rank 2 "endpoint" theory
arxiv created 2018/06/03 · arxiv updated 2018/06/05
We formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose an exhaustive classification of local 3-folds engineering rank 2 SCFTs in 5d. This systematic classification confirms that all rank 2 SCFTs predicted using gauge theoretic arguments can be realized as consistent theories, with the exception of one family which is shown to be non-perturbatively inconsistent and thereby ruled out by geometric considerations. We find that all rank 2 SCFTs descend from 6d (1,0) SCFTs compactified on a circle possibly twisted with an automorphism together with holonomies for global symmetries around the Kaluza-Klein circle. These results support our conjecture that every 5d SCFT can be obtained from the circle compactification of some parent 6d (1,0) SCFT.