Virasoro Symmetry in Neural Network Field Theories

• URL: http://arxiv.org/abs/2512.24420v1
• Date: Tue, 30 Dec 2025 19:00:01 GMT
• Title: Virasoro Symmetry in Neural Network Field Theories
• Authors: Brandon Robinson,
• Abstract summary: We present the first construction of an NN-FT that encodes the full Virasoro symmetry of a 2d CFT.<n>We then construct an NN realization of a Majorana Fermion and an $mathcalN= (1,1)$ scalar multiplet.<n>We extend the framework by constructing boundary NN-FTs that preserve (super-)conformal symmetry via the method of images.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural Network Field Theories (NN-FTs) can realize global conformal symmetries via embedding space architectures. These models describe Generalized Free Fields (GFFs) in the infinite width limit. However, they typically lack a local stress-energy tensor satisfying conformal Ward identities. This presents an obstruction to realizing infinite-dimensional, local conformal symmetry typifying 2d Conformal Field Theories (CFTs). We present the first construction of an NN-FT that encodes the full Virasoro symmetry of a 2d CFT. We formulate a neural free boson theory with a local stress tensor $T(z)$ by properly choosing the architecture and prior distribution of network parameters. We verify the analytical results through numerical simulation; computing the central charge and the scaling dimensions of vertex operators. We then construct an NN realization of a Majorana Fermion and an $\mathcal{N}=(1,1)$ scalar multiplet, which then enables an extension of the formalism to include super-Virasoro symmetry. Finally, we extend the framework by constructing boundary NN-FTs that preserve (super-)conformal symmetry via the method of images.

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