Form factors and spectral densities from Lightcone Conformal Truncation

Abstract

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators \U0001d4aa in ϕ4 theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator \U0001d4aa between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of \U0001d4aa between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator \U0001d4aa is the trace Θ of the stress tensor.