AdS N-body problem at large spin

A bstract Motivated by the problem of multi-twist operators in general CFTs, we study the leading-twist states of the N -body problem in AdS at large spin J . We find that for the majority of states the effective quantum-mechanical problem becomes semiclassical with ℏ = 1/ J . The classical system at J = ∞ has N − 2 degrees of freedom, and the classical phase space is identified with the positive Grassmannian Gr + (2, N ). The quantum problem is recovered via a Berezin-Toeplitz quantization of a classical Hamiltonian, which we describe explicitly. For N = 3 the classical system has one degree of freedom and a detailed structure of the spectrum can be obtained from Bohr-Sommerfeld conditions. For all N , we show that the lowest excited states are approximated by a harmonic oscillator and find explicit expressions for their energies.