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1. Instanton resummation and the Weak Gravity Conjecture

   https://doi.org/10.1007/JHEP11(2020)166  

   Heidenreich, Ben; Long, Cody; McAllister, Liam; Rudelius, Tom; Stout, John (November 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract We develop methods for resummation of instanton lattice series. Using these tools, we investigate the consequences of the Weak Gravity Conjecture for large-field axion inflation. We find that the Sublattice Weak Gravity Conjecture implies a constraint on the volume of the axion fundamental domain. However, we also identify conditions under which alignment and clockwork constructions, and a new variant of N -flation that we devise, can evade this constraint. We conclude that some classes of low-energy effective theories of large-field axion inflation are consistent with the strongest proposed form of the Weak Gravity Conjecture, while others are not. 

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2. Moduli space reconstruction and Weak Gravity

   https://doi.org/10.1007/JHEP12(2023)134  

   Gendler, Naomi; Heidenreich, Ben; McAllister, Liam; Moritz, Jakob; Rudelius, Tom (December 2023, Journal of High Energy Physics)

   We present a method to construct the extended Kähler cone of any Calabi-Yau threefold by using Gopakumar-Vafa invariants to identify all geometric phases that are related by flops or Weyl reflections. In this way we obtain the Kähler moduli spaces of all favorable Calabi-Yau threefold hypersurfaces with h1,1 ≤ 4, including toric and non-toric phases. In this setting we perform an explicit test of the Weak Gravity Conjecture by using the Gopakumar-Vafa invariants to count BPS states. All of our examples satisfy the tower/sublattice WGC, and in fact they even satisfy the stronger lattice WGC. 

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3. Weak gravity conjecture

   https://doi.org/10.1103/RevModPhys.95.035003  

   Harlow, Daniel; Heidenreich, Ben; Reece, Matthew; Rudelius, Tom (September 2023, Reviews of Modern Physics)

   The weak gravity conjecture holds that in a theory of quantum gravity any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. These related conjectures and the evidence for their validity in the string theory landscape are reviewed. Also reviewed are a variety of arguments for these conjectures, which tend to fall into two categories: qualitative arguments that claim the conjecture is plausible based on general principles and quantitative arguments for various special cases or analogs of the conjecture. The implications of these conjectures for particle physics, cosmology, general relativity, and mathematics are also outlined. Finally, important directions for future research are highlighted. 

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4. Conway subgroup symmetric compactifications redux

   https://doi.org/10.1007/JHEP03(2022)142  

   Baykara, Zihni Kaan; Harvey, Jeffrey A. (March 2022, Journal of High Energy Physics)

   A bstract We extend the investigation in [1] of special toroidal compactifications of heterotic string theory for which the half-BPS states provide representations of subgroups of the Conway group. We also explore dual descriptions of these theories and find that they are all linked to either F-theory or type IIA string theory on K3 surfaces with symplectic automorphism groups that are the same Conway subgroups as those of the heterotic dual. The matching with type IIA K3 dual theories includes both the matching of symmetry groups and a comparison between the Narain lattice on the heterotic side and the cohomology lattice on the type IIA side. We present twelve examples where we can identify a type IIA dual K3 orbifold theory as the dual description of the heterotic theory. In addition, we include a supplementary Mathematica package that performs most of the computations required for these comparisons. 

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5. Theory of oblique topological insulators

   https://doi.org/10.21468/SciPostPhys.14.2.023  

   Moy, Benjamin; Goldman, Hart; Sohal, Ramanjit; Fradkin, Eduardo (January 2023, SciPost Physics)

   A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional 𝜃-angles,long-range entanglement, and fractionalization. Starting from a simple family of ℤ_N lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons—bound states of electric charges and monopoles—condense, leading to FTI phases characterized by topological order, emergent one-forms symmetries, and gapped boundary states not realizable in 2+1-D alone.Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal “generalized magneto-electric effect” in the presence of two-form background gauge fields. Moreover,we characterize the possible boundary topological orders of oblique TIs,finding a new set of boundary states not studied previously for these kinds of TQFTs. 

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