Topological Effects in Neural Network Field Theory
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on $S^1$, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement...
| Authors | Christian Ferko, James Halverson, Vishnu Jejjala et al. |
|---|---|
| Primary category | hep-th |
| Published | 2 April 2026 |
| Last updated at source | 2 April 2026 |
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