Reconstructing conformal field theoretical compositions with Transformers

TL;DR

This paper demonstrates that transformers can effectively reconstruct tensor product compositions of 2D rational conformal field theories from low-energy spectra, achieving high accuracy and generalizing to unseen cases.

Contribution

The authors introduce a transformer-based method for reconstructing RCFT compositions, achieving 98% accuracy and demonstrating generalization to larger central charges and unseen classes.

Findings

Achieved 98% accuracy in reconstructing tensor product theories.

Method generalizes to larger central charges and unseen RCFT classes.

Transformers show promise as a tool for bulk reconstruction in AdS/CFT.

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.