Topic: gapless boundaries

Liang Kong reviews a unified mathematical treatment of gapped and gapless boundaries in topological orders in two spatial dimensions. It leads to topological Wick rotation, proposed as a broader organising principle for suitable quantum field theories. The talk examines generalisations and applications, including how familiar topological holography and sandwich constructions emerge as special cases.

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.