F-theory and the Classification of LSTs Tom Rudelius Harvard University

Based On 1502.05405/hep-th with Jonathan Heckman, David Morrison*, and Cumrun Vafa 1511.05565/hep-th with Lakshya Bhardwaj, Michele Del Zotto, Jonathan Heckman, David Morrison*, and Cumrun Vafa *A very happy belated 60th birthday to Dave

Recall from Jonathan Heckman’s Talk: 6D SCFTs have been classified via F-theory Nearly all F-theory conditions can be phrased in field theory terms 6D SCFTs = Generalized Quivers

Recall from Jonathan Heckman’s Talk: Looks like chemistry “Radicals” “Atoms”

Classification Strategy

Why study LSTs? LSTs serve as “toy model” for full string theory LSTs sit between SCFTs and gravitational theories in 6D Understanding LSTs will help us understand these theories in more detail

They are characterized by the presence of a non- dynamical tensor Punchline #1 LSTs are UV complete, non-local 6D theories with gravity decoupled and an intrinsic string scale They are characterized by the presence of a non- dynamical tensor

LSTs are “affinizations” of 6D SCFTs Punchline #2 LSTs are “affinizations” of 6D SCFTs

Punchline #3 Gauge algebras and matter content of 6D LSTs are tightly constrained by anomaly cancellation (similar to 6D SCFTs)

Punchline #4 F-theory models of many LSTs feature a total space with two elliptic fibrations

“Affinizing” SCFTs

Example: (2,0) LSTs SCFTs LSTs

A (1,0) Example SCFT LST

Enhancing SCFT Fibers Enhancing LST Fibers 16 fundamentals, 2 antisym. tensors + 2 fundamentals adjoint hyper + 2 fundamentals 16 fundamentals, 2 antisym. tensors adjoint hyper

adjoint hyper 16 fundamentals 1 antisym. tensor

Conclusions LSTs are 6D theories with gravity decoupled, a non-dynamical tensor, and an intrinsic string scale The classification of 6D SCFTs enables the classification of LSTs via “affinization” Known T-dualities between LSTs are realized in F-theory as exchange of a double elliptic fibration

Open Questions Non-geometric structures in F-theory? Compactifications of LSTs? RG flows for LSTs? T-duality of general LSTs?