Reconstructing conformal field theoretical compositions with Transformers
Abstract
We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The constituent theories are characterized by their central charges and affine Lie algebra labels. We achieve 98% accuracy in recovering the constituents of tensor products theories constructed from Wess-Zumino-Witten models. We further demonstrate that our method generalizes to CFTs with larger central charge and unseen classes of RCFTs by adding a small number of out-of-domain examples. Our results show that transformers are effective at this task and point towards a new tool for bulk reconstruction in AdS/CFT.
Cite
@article{arxiv.2605.01072,
title = {Reconstructing conformal field theoretical compositions with Transformers},
author = {Haotian Cao and Garrett Merz and Kyle Cranmer and Gary Shiu},
journal= {arXiv preprint arXiv:2605.01072},
year = {2026}
}