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1. JAXVacua — a framework for sampling string vacua

   https://doi.org/10.1007/JHEP12(2023)146  

   Dubey, A; Krippendorf, S; Schachner, A (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> Moduli stabilisation in string compactifications with many light scalars remains a major blind-spot in the string landscape. In these regimes, analytic methods cease to work for generic choices of UV parameters which is why numerical techniques have to be exploited. In this paper, we implement algorithms based on JAX, heavily utilising automatic differentiation, just-in-time compilation and parallelisation features, to efficiently construct string vacua. This implementation provides a golden opportunity to efficiently analyse large unexplored regions of the string landscape. As a first example, we apply our techniques to the search of Type IIB flux vacua in Calabi-Yau orientifold compactifications. We argue that our methods only scale mildly with the Hodge numbers making exhaustive studies of low energy effective field theories with$$ \mathcal{O} $$ $O$(100) scalar fields feasible. Using small computing resources, we are able to construct$$ \mathcal{O} $$ $O$(10⁶) flux vacua per geometry withh^1,2≥ 2, vastly out-performing previous systematic searches. In particular, we showcase the efficiency of our methods by presenting generic vacua with fluxes below the tadpole constraint set by the orientifold with up toh^1,2= 25 complex structure moduli. 

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2. The frozen phase of heterotic F-theory duality

   https://doi.org/10.1007/JHEP07(2024)295  

   Oehlmann, Paul-Konstantin; Ruehle, Fabian; Sung, Benjamin (July 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We study the duality between the Spin(32)/ℤ₂heterotic string without vector structure and F-theory with frozen singularities. We give a complete description in theories with 6d$$ \mathcal{N} $$ $N$= (1, 0) supersymmetry and identify the duals of Spin(32)/ℤ₂-instantons on ADE singularities without vector structure in the frozen phase of F-theory using an ansatz introduced by Bhardwaj, Morrison, Tachikawa, and Tomasiello. As a consequence, we obtain a strongly coupled description of orbifold phases of type I string theory without vector structure, substantially expanding the list of known examples of 6d F-theory compactifications with frozen singularities. Supergravity theories can befusedfrom these instanton theories, in a way that commutes with switching off vector structure, which we use to propose new consistency checks via neutral hypermultiplet counting. Finally, we describe various Higgsings of this duality, and comment on constraints on higher form symmetries. 

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3. Bounds on field range for slowly varying positive potentials

   https://doi.org/10.1007/JHEP02(2024)175  

   van_de_Heisteeg, Damian; Vafa, Cumrun; Wiesner, Max; Wu, David H (February 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that$$ V<{\Lambda}_s^2 $$ $V<{\Lambda }_s^2$, where Λ_s(ϕ) is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: ∆ϕ≤alog(1/V) +bin Planck units, wherea≤$$ \sqrt{\left(d-1\right)\left(d-2\right)} $$ $\sqrt{\left(d-1\right)\left(d-2\right)}$, andbis an 𝒪(1) number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi-Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constantb, which we verify is 𝒪(1) and negative in all the examples we studied. 

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4. BPS Algebras in 2D String Theory

   https://doi.org/10.1007/s00023-022-01189-7  

   Harrison, Sarah M.; Paquette, Natalie M.; Persson, Daniel; Volpato, Roberto (May 2022, Annales Henri Poincaré)

   Abstract We discuss a set of heterotic and type II string theory compactifications to$$1+1$$ $1+1$dimensions that are characterized by factorized internal worldsheet CFTs of the form$$V_1\otimes \bar{V}_2$$ $V_1\otimes {\overline{V}}_2$, where$$V_1, V_2$$ $V_1,V_2$are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications. 

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5. New non-supersymmetric flux vacua in string theory

   https://doi.org/10.1007/JHEP12(2023)145  

   Krippendorf, S; Schachner, A (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in [1] for which we provide the first explicit examples in Calabi-Yau orientifold compactifications with discrete fluxes below their respective tadpole constraint. As a proof of concept, we study the degree 18 hypersurface in weighted projective space$$ \mathbbm{CP} $$ $\mathrm{CP}$_1,1,1,6,9. Furthermore, we look at 10 additional orientifolds withh^1,2= 2,3. We find several flux vacua with hierarchical suppression of the vacuum energy with respect to the gravitino mass. These solutions provide a crucial stepping stone for the construction of explicit de Sitter vacua in string theory. Lastly, we also report the difference in the distribution ofW₀between supersymmetric and non-supersymmetric minima. 

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