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 $\mathcal{O}$ in ${\varphi }^4$ 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 $\mathcal{O}$ 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 $\mathcal{O}$ 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 $\mathcal{O}$ is the trace $\Theta$ of the stress tensor.

arXiv comment32 pages+ appendices, 16 figures

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• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Towards a nonperturbative construction of the $S$-matrix
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Lightcone Hamiltonian for Ising Field Theory I: T < T_c
• Chiral Limit of 2d QCD Revisited with Lightcone Conformal Truncation