We consider flux vacua for type IIB orientifold compactifications and study their interplay with the tadpole‐cancellation condition. As a concrete example we focus on double-struckT6/double-struckZ2×double-struckZ2, for which we find that solutions to the F‐term equations at weak coupling, large complex structure and large volume require large flux contributions. Such contributions are however strongly disfavored by the tadpole‐cancellation condition. We furthermore find that solutions which stabilize moduli in this perturbatively‐controlled regime are only a very small fraction of all solutions, and that the space of solutions is not homogenous but shows characteristic void structures and vacua concentrated on submanifolds.

Dualities are widely used in quantum field theories and string theory to obtain correlation functions at high accuracy. Here we present examples where dual data representations are useful in supervised classification, linking machine learning and typical tasks in theoretical physics. We then discuss how such beneficial representations can be enforced in the latent dimension of neural networks. We find that additional contributions to the loss based on feature separation, feature matching with respect to desired representations, and a good performance on a 'simple' correlation function can lead to known and unknown dual representations. This is the first proof of concept that computers can find dualities. We discuss how our examples, based on discrete Fourier transformation and Ising models, connect to other dualities in theoretical physics, for instance Seiberg duality.

We perform dimensional reductions of type IIA and type IIB double field theory in the flux formulation on Calabi-Yau three-folds and on K3 × T 2 . In addition to geometric and non-geometric three-index fluxes and Ramond-Ramond fluxes, we include generalized dilaton fluxes. We relate our results to the scalar potentials of corresponding four-dimensional gauged supergravity theories, and we verify the expected behavior under mirror symmetry. For Calabi-Yau three-folds we extend this analysis to the full bosonic action including kinetic terms. Basics of Double Field TheoryThis section will provide a brief overview on the notions of DFT, which form the basis of our upcoming considerations. For more details, we would like to refer the reader to [26-28]. Doubled SpacetimeThe basic idea of DFT is to enhance ordinary supergravity theories with additional structures in a way that T-duality becomes a manifest symmetry. Motivated by the insights from toroidal compactifications of the bosonic string, one doubles the dimension of the D-dimensional spacetime manifold M by introducing additional winding coordinatesxm conjugate to the winding numberpm (just as the normal spacetime coordinates xm relate to the momenta pm) and arrange them in doubled coordinates XM = xm, xm , PM = pm, pm withm = 1, . . . D andM = 0, . . . 2D. (2.1)

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