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

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

3. 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

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

5. Classification Strategy

7. 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

8. 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

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

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

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

23. “Affinizing” SCFTs

24. Example: (2,0) LSTs
SCFTs
LSTs

25. A (1,0) Example
SCFT
LST

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

29. adjoint hyper
16 fundamentals
1 antisym. tensor

31. 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

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