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In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher‐form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement thatd‐dimensional quantum field theories with global ‐form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non‐invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher‐form symmetries, which can be used to select individual universes in a decomposition.

In large‐eddy simulations, subgrid‐scale (SGS) processes are parameterized as a function of filtered grid‐scale variables. First‐order, algebraic SGS models are based on the eddy‐viscosity assumption, which does not always hold for turbulence. Here we apply supervised deep neural networks (DNNs) to learn SGS stresses from a set of neighboring coarse‐grained velocity from direct numerical simulations of the convective boundary layer at friction Reynolds numbersRe_τup to 1243 without invoking the eddy‐viscosity assumption. The DNN model was found to produce higher correlation between SGS stresses compared to the Smagorinsky model and the Smagorinsky‐Bardina mixed model in the surface and mixed layers and can be applied to different grid resolutions and various stability conditions ranging from near neutral to very unstable. The DNN model can capture key statistics of turbulence ina posteriori(online) tests when applied to large‐eddy simulations of the atmospheric boundary layer.

Motivated by its potential use as a starting point for solving various cosmological constant problems, we study F‐theory compactified on the warped productwhereY₈is amanifold, and theS³factor is the target space of anWess–Zumino–Witten (WZW) model at levelN. Reduction to M‐theory exploits the abelian duality of this WZW model to anorbifold. In the largeNlimit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7‐branes in thegeometry is controlled by a Donaldson–Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as “supersymmetry” on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of orderspecified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.

We study the phenomenology of a recent string construction with a quantum mechanically stable dark energy. A mild supersymmetry protects the vacuum energy but also allowsTeV scale superpartner masses. The construction is holographic in the sense that the 4D spacetime is generated from “spacetime pixels” originating from five‐branes wrapped over metastable five‐cycles of the compactification. The cosmological constant scales asin the pixel number. An instability in the construction leads to cosmic expansion. This also causes more five‐branes to wind up in the geometry, leading to a slowly decreasing cosmological constant which we interpret as an epoch of inflation followed by (pre‐)heating when a rare event occurs in which the number of pixels increases by an order one fraction. The sudden appearance of radiation triggers an exponential increase in the number of pixels. Dark energy has a time varying equation of state with, which is compatible with current bounds, and could be constrained further by future data releases. The pixelated nature of the Universe also implies a large‐lcutoff on the angular power spectrum of cosmological observables with. We also use this pixel description to study the thermodynamics of de Sitter space, finding rough agreement with effective field theory considerations.