Form factors and spectral densities from Lightcone Conformal Truncation

Abstract

Abstract We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators 𝒪 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 𝒪 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 𝒪 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 𝒪 is the trace Θ of the stress tensor.