Radial lattice quantization of 3D Φ⁴ field theory

Journal Article · 05 November 2021 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.104.094502 · OSTI ID:1829176

Brower, Richard C. ^[1]; Fleming, George T.  ^[2]; Gasbarro, Andrew D. ^[3]; Howarth, Dean ^[4]; Raben, Timothy G.  ^[5]; Tan, Chung-I ^[6]; Weinberg, Evan S. ^[7]

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1. Boston Univ., MA (United States)
2. Yale Univ., New Haven, CT (United States)
3. Univ. of Bern (Switzerland)
4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
5. Michigan State Univ., East Lansing, MI (United States)
6. Brown Univ., Providence, RI (United States)
7. NVIDIA Corporation, Santa Clara, CA (United States)

The quantum extension of classical finite elements, referred to as quantum finite elements, is applied to the radial quantization of 3d Φ⁴ theory on a simplicial lattice for the $$\mathbb{R}$$ × $$\mathbb{S}$$² manifold. Explicit counter terms to cancel the one- and two-loop ultraviolet defects are implemented to reach the quantum continuum theory. Using the Brower-Tamayo cluster Monte Carlo algorithm, numerical results support the QFE ansatz that the critical conformal field theory (CFT) is reached in the continuum with the full isometries of $$\mathbb{R}$$ × $$\mathbb{S}$$² restored. The Ricci curvature term, while technically irrelevant in the quantum theory, is shown to dramatically improve the convergence opening, the way for high precision Monte Carlo simulation to determine the CFT data: operator dimensions, trilinear OPE couplings and the central charge.

• Research Organization: Boston Univ., MA (United States)
• Sponsoring Organization: USDOE; Swiss National Science Foundation (SNSF)
• Grant/Contract Number: SC0015845; SC0019061; 200021_175761
• OSTI ID: 1829176
• Alternate ID(s): OSTI ID: 1833383
• Journal Information: Physical Review. D., Vol. 104, Issue 9; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English