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 SLEκ​ bubble measure, the
coupling between SLE and Liouville quantum gravity, and the integrability of
Liouville conformal field theory. Along the way, we derive a formula not only
for κ=6 (corresponding to percolation), but for all κ∈(4,8).Comment: 63 pages, 17 figure