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  • Open Access

Swampland cobordism conjecture and non-Abelian duality groups

Markus Dierigl* and Jonathan J. Heckman†

  • Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • *markusd@sas.upenn.edu
  • †jheckman@sas.upenn.edu
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Phys. Rev. D 103, 066006 – Published 3 March, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.066006

Abstract

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group SL(2,Z) implies the existence of additional [p,q] 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover the full structure of non-Abelian braid statistics for 7-branes. Combining the cobordism conjecture with an earlier Swampland conjecture by Ooguri and Vafa, we argue that only certain congruence subgroups Γ⊂SL(2,Z) specifying genus zero modular curves can appear in 8D F-theory vacua. This leads to a successful prediction for the allowed Mordell–Weil torsion groups for 8D F-theory vacua.

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Phys. Rev. D 103, 066006– Published 3 March, 2021
  • Received 5 January 2021
  • Accepted 10 February 2021
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