Journal of High Energy Physics

, 2015:52 | Cite as

Geometry of 6D RG flows

  • Jonathan J. Heckman
  • David R. Morrison
  • Tom Rudelius
  • Cumrun Vafa
Open Access
Regular Article - Theoretical Physics


We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: one corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as resolving the base of the geometry. The other corresponds to giving expectation values to hypermultiplets (Higgs branch flow) realized as complex structure deformations of the geometry. To corroborate this physical picture we calculate the change in the anomaly polynomial for these theories, finding strong evidence for a flow from a UV fixed point to an IR fixed point. Moreover, we find evidence against non-trivial dualities for 6D SCFTs. In addition we find non-trivial RG flows for theories realizing small E 8 instantons on ALE spaces.


F-Theory Differential and Algebraic Geometry Conformal and W Symmetry Field Theories in Higher Dimensions 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Jonathan J. Heckman
    • 1
  • David R. Morrison
    • 2
    • 3
  • Tom Rudelius
    • 4
  • Cumrun Vafa
    • 4
  1. 1.Department of PhysicsUniversity of North CarolinaChapel HillUnited States
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraUnited States
  3. 3.Department of PhysicsUniversity of CaliforniaSanta BarbaraUnited States
  4. 4.Jefferson Physical LaboratoryHarvard UniversityCambridgeUnited States

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