Descending into the Modular Bootstrap
In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus partition function of a 2d CFT is fixed by the spectrum of its primary operators and its chiral algebra, which we take to be the Virasoro algebra with $c>1$. We translate the requirement that this partition function is modular invariant into a loss function, which we then minimize to identify possible primary spectra. Our approach involves two technical innovations that facilitate finding reliable candidate CFTs. The first is a strategy to estimate the...
| Authors | Nathan Benjamin, A. Liam Fitzpatrick, Wei Li et al. |
|---|---|
| Primary category | hep-th |
| Published | 1 April 2026 |
| Last updated at source | 2 August 2026 |
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