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# (09.05.) Geometry, Modularity, and Quantum Gravity Conjectures

### Seung-Joo Lee (Cern)

#### 09.05.2019 at 16:15

We test various conjectures on quantum gravity in the context of string theory, focusing mostly on general six-dimensional EFTs of F-theory for concreteness. Starting with a gauge theory coupled to gravity, we first analyze the limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. A key observation is made about the appearance of a tensionless string in such a limit. For a more quantitative analysis, we focus on a U(1) gauge dynamics and look into the elliptic genus of this string in terms of certain meromorphic weak Jacobi forms, of which modular properties allow us to determine the charge-to-mass ratios of certain string excitations. A tower of these asymptotically massless charged states are then confirmed to satisfy the (sub-)Lattice Weak Gravity Conjecture, the Completeness Conjecture, and the Swampland Distance Conjecture. We interpret their charge-to-mass ratios in two a priori independent perspectives. If time permits, some generalizations will also be presented, extending the story to multiple U(1)s, to two-form dynamics, as well as to four dimensions.

Arnold Sommerfeld Center

Theresienstrasse 37

Room 348