Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Using canonical 1-parameter family of Hermitian connections on the tangent bundle, we provide invariant solutions to the Strominger system on complex Lie groups. Both flat and non-flat cases are discussed in detail.Comment: 11 pages, comments are welcome. Updates in v2: minor typos are corrected. Updates in v3: small revisions, to be consistent with published versio

Three dimensional canonical singularity and five dimensional N=1 SCFT

We conjecture that every three dimensional canonical singularity defines a five dimensional N=1 SCFT. Flavor symmetry can be found from singularity structure: non-abelian flavor symmetry is read from the singularity type over one dimensional singular locus. The dimension of Coulomb branch is given by the number of compact crepant divisors from a crepant resolution of singularity. The detailed structure of Coulomb branch is described as follows: a): A chamber of Coulomb branch is described by a crepant resolution, and this chamber is given by its Nef cone and the prepotential is computed from triple intersection numbers; b): Crepant resolution is not unique and different resolutions are related by flops; Nef cones from crepant resolutions form a fan which is claimed to be the full Coulomb branch.Comment: 35 pages, 17 figure