The boundary conjecture for anomaly-free rational conformal field theories

An RCFT has vanishing gravitational anomaly when its left- and right-moving gravitational anomaly cancels. A boundary condition has finite $g$-function when its boundary entropy parameter $g$ is finite. RCFT boundary conjecture. Every RCFT with vanishing gravitational anomaly admits a boundary condition with finite $g$-function. The conjecture is a special case of the folklore expectation that anomalies are the only obstruction to connecting quantum field theories by continuous deformations.