2024/12/16 by Kravchuk, Petr, Mann, Jeremy A. · 2 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2412.12328
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.