Bootstrapping 2d ϕ⁴ theory with Hamiltonian truncation data

Journal Article · 17 February 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2022)146 · OSTI ID:1976451

Chen, Hongbin  ^[1]; Fitzpatrick, A. Liam ^[2]; Karateev, Denis ^[3]

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1. Boston Univ., MA (United States); Boston Univ., MA (United States)
2. Boston Univ., MA (United States)
3. Univ. Paris-Saclay, Paris (France). Philippe Meyer Institute, Physics Department École Normale Supérieure (ENS)

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ⁴ theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ⁴ two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

• Research Organization: Boston Univ., MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0015845
• OSTI ID: 1976451
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English