  We study the three-body system with short-range interactions characterized by
an unnaturally large two-body scattering length. We show that the off-shell
scattering amplitude is cutoff independent up to power corrections. This allows
us to derive an exact renormalization group equation for the three-body force.
We also obtain a renormalized equation for the off-shell scattering amplitude.
This equation is invariant under discrete scale transformations. The
periodicity of the spectrum of bound states originally observed by Efimov is a
consequence of this symmetry. The functional dependence of the three-body
scattering length on the two-body scattering length can be obtained
analytically using the asymptotic solution to the integral equation. An
analogous formula for the three-body recombination coefficient is also
obtained.
