Brief

Researchers have developed a novel method to explore two-dimensional conformal field theories (2d CFTs) by using machine-learning-inspired optimization techniques to solve the modular bootstrap equation. This approach efficiently searches for numerical solutions, identifying potential primary operator spectra by minimizing a loss function derived from modular invariance. The study introduces innovations like a strategy for estimating spectral truncation uncertainty and a new singular-value-based optimizer named Sven, which proves more effective than gradient descent for navigating complex loss landscapes. The team successfully constructed candidate partition functions for CFTs with central charges between 1 and 8/7, a region previously lacking known examples, suggesting the existence of a continuous space of modular bootstrap solutions. AI