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1. 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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2. Recent Developments in Line Bundle Cohomology and Applications to String Phenomenology

   Brodie, Callum; Constantin, Andrei; Gray, James; Lukas, Andre; Ruehle, Fabian (September 2022, Nankai Symposium on Mathematical Dialogues)

   He, Yang-Hui; Ge, Mo-Lin; Bai, Cheng-Ming; Bao Jiakang; Hirst, Edward (Ed.)

   Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for performing cohomology calculations, they are laborious and ill-suited for scanning over large sets of string compactifications to find those most relevant to particle physics. In this article we review some recent progress in deriving closed-form expressions for line bundle cohomology and discuss some applications to string phenomenology. 

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3. Small cosmological constants in string theory

   https://doi.org/10.1007/JHEP12(2021)136  

   Demirtas, Mehmet; Kim, Manki; McAllister, Liam; Moritz, Jakob; Rios-Tascon, Andres (December 2021, Journal of High Energy Physics)

   A bstract We construct supersymmetric AdS 4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α ′ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10 − 123 in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol. 

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4. On the number of p-hypergeometric solutions of KZ equations

   https://doi.org/10.1007/s11139-022-00659-0  

   Varchenko, Alexander (January 2022, The Ramanujan Journal)

   We consider the master functions associated with one irreducible integrable highest weight representation of a Kac-Moody algebra. We study the generation procedure of new critical points from a given critical point of one of these master functions. We show that all critical points of all these master functions can be generated from the critical point of the master function with no variables. In particular this means that the set of all critical points of all these master functions form a single population of critical points. We formulate a conjecture that the number of populations of critical points of master functions associated with a tensor product of irreducible integrable highest weight representations of a Kac-Moody algebra are labeled by homomorphisms to $$\C$$ of the Bethe algebra of the Gaudin model associated with this tensor product. 

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5. $$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization

   https://doi.org/10.1007/JHEP12(2019)119  

   Binder, Damon J.; Chester, Shai M.; Pufu, Silviu S.; Wang, Yifan (December 2019, Journal of High Energy Physics)

   A bstract We compute 1 /λ corrections to the four-point functions of half-BPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in the limit where N is taken to be large while g YM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S 4 partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes. 

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