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 O in φ 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 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.

Chiral Limit of 2d QCD Revisited with Lightcone Conformal Truncation

“…Because of the truncation of the Hilbert space, the spectrum of eigenvalues is discrete and a literal implementation of the spectral density (3.11) produces a discrete approximation of the true c-function. We can interpolate the c-function by taking advantage of the analyticity of the time-ordered correlator [21]. First, we use the discrete spectral density ρ T −− (µ i ) to compute the time-ordered correlator…”

Hamiltonian Truncation with Larger Dimensions

“…[2] computed the spectrum of the two-dimensional Ising model perturbed by its most relevant operator, and [3] computed the spectrum of the two-dimensional Tricritical Ising model perturbed by each of its relevant primaries. 1 Hamiltonian Truncation has since been applied in a variety of other contexts, for instance to QFTs quantised on the light-cone [4][5][6][7][8], to analyse RG flows on the sphere [9], QFTs on an AdS background [10] and used in combination with the S-matrix bootstrap to analyse form factors [11,12]. In [13], the first HT spectrum computation in d > 2 spacetime dimensions was carried out for the free-boson CFT perturbed by the m 2 φ 2 + λφ 4 operators.…”