Backbone exponent for two-dimensional percolation

Understand

We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality.

• It turns out to be a root of an elementary function.
• Contrary to previously known arm exponents for this model, which are all rational, it has a transcendental value.
• Our derivation relies on the connection to the SLE$_\kappa$ bubble measure, the coupling between SLE and Liouville quantum gravity, and the integrability of Liouville conformal field theory.