We conjecture that meanders are governed by the gravitational version of a c = - 4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent (formula presented), and the semi-meander exponent (formula presented) This result follows from an interpretation of meanders as pairs of fully packed loops on a random surface, described by two c = - 2 free fields. The above values agree with recent numerical estimates. We generalize these results to a score of meandric numbers with various geometries and arbitrary loop fugacities.
- 2D quantum gravity
- Coulomb gas
- Fully packed loop models
ASJC Scopus subject areas
- Nuclear and High Energy Physics