Topic: conformal field theories

The conformal bootstrap studies strongly coupled quantum field theories through symmetry, unitarity and crossing symmetry without relying on perturbation theory. This talk reviews recent analytic functional approaches to the numerical bootstrap and introduces new results. It then considers how machine learning could navigate consistent conformal field theories. Neural networks can construct crossing-symmetric correlators from limited physical input; their tendency toward simple, smooth solutions may reveal additional organizing principles behind bootstrap constraints.

Xiang Li presents an entanglement-bootstrap programme for two-dimensional chiral gapped phases. Entanglement conditions yield features such as robust gapless boundaries and sharp-corner entropy contributions. Instantaneous modular flow provides a quantum-information primitive for relations between local entanglement Hamiltonians and produces equations generalising topological-entropy and chiral-central-charge formulas. Applications to conformal field theories in one and two spatial dimensions are also discussed.