Form factors and spectral densities from Lightcone Conformal Truncation

Hongbin Chen (Department of Physics, Boston University, Boston, MA, 02215, USA) ; A. Fitzpatrick (Department of Physics, Boston University, Boston, MA, 02215, USA) ; Denis Karateev (Philippe Meyer Institute, Physics Department École Normale Supérieure (ENS), Université PSL24 rue Lhomond, Paris, F-75231, France)

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.

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      "surname": "Fitzpatrick", 
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      "surname": "Karateev", 
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      "source": "Springer", 
      "value": "We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators \ud835\udcaa in \u03d5 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 \ud835\udcaa 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 \ud835\udcaa 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 \ud835\udcaa is the trace \u0398 of the stress tensor."
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Published on:
20 April 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 4
Pages 1-39
DOI:
https://doi.org/10.1007/JHEP04(2022)109
arXiv:
2107.10285
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: