Aug 2026· AI in Mathematics and Theoretical Physics· pp. 1-11· 1 citation· 22 references
Physics
Abstract
Neural network field theory (NN-FT) defines a field theory by a network architecture together with a probability density on its latent variables. For compact theories the local Gaussian sector is only part of the story: one must also sum over discrete topological sectors. We review a mixed continuous/discrete latent-variable construction and apply it to two compact bosons. For the Berezinskii–Kosterlitz–Thouless transition, a random Fourier feature spin-wave sampler supplemented by an explicit Coulomb gas vortex sector reproduces the Gaussian critical line below [Formula: see text], vortex proliferation above [Formula: see text], the essential singularity of the correlation length, and the Nelson–Kosterlitz jump. For the bosonic string, oscillator modes augmented by momentum–winding labels reproduce circle T-duality, Buscher transformations on constant toroidal backgrounds, self-dual current algebra enhancement, and a toy T-fold. The common lesson is that the same local neural sampler, paired with different discrete topological data, yields physically distinct compact theories. These proceedings are based on [1].
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Planar parity-preserving tensor networks (ppTNs) admit a fermionic formulation in which the Gaussian, efficiently contractible limit is deformed by local interactions. We investigate how many-body methods can be used to analyze such contractions in a minimal two-parameter ppTN. Its contraction is simultaneously an inte...
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Computing boson star families traditionally requires repeated solution of nonlinear eigenvalue boundary-value problems and careful numerical continuation through turning points. We develop a physics-informed neural network (PINN) that learns the map from the physical parameters and radial coordinate directly to the sca...
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We derive thermal Polyakov bootstrap equations for CFT two-point functions on $S^1_\beta\times\mathbb R^{d-1}$. Combining the thermal OPE with a dispersion relation and the method of images gives a representation in blocks that satisfy Kubo-Martin-Schwinger (KMS) covariance. Their local expansions contain additional th...
