Particle theory

Abstract:

Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation-the canonical use cases-provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.

Abstract:

We study heterotic Calabi-Yau compactifications with NSNS three-form flux in view of moduli stabilisation and investigate whether the value |W0| of the flux superpotential evaluated at supersymmetric minima can be small. Unlike in type IIB string theory, heterotic compactifications lack a no-scale structure, so that a non-vanishing flux superpotential generically induces a tree-level scalar potential for all moduli. Controlled moduli stabilisation therefore requires the flux superpotential to be sufficiently small in order to compete with non-perturbative effects. Working within a four-dimensional effective field theory and exploiting the special geometry of Calabi-Yau complex structure moduli spaces, we analyse the complex structure F-term equations and derive two no-go theorems: (1) supersymmetric vacua with vanishing |W0|, which would lead to a vanishing tree-level scalar potential as in type IIB, occur only at singular loci in moduli space, and (2) no supersymmetric vacua with small |W0| exist in the large complex structure limit. Motivated by these results, we analyse explicit models away from the large complex structure regime using exact period expressions and identify one- and two-parameter examples in which suitable flux choices allow for values of |W0| of order unity, with some one-parameter models admitting values moderately below unity. Our findings show that small heterotic flux superpotentials are highly constrained, with the values of |W0| found in the examples studied being only marginally compatible with moduli stabilisation.