Title: Radial lattice quantization of 3D ${\varphi }^4$ field theory

Abstract

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.

Authors:

Brower, Richard C.; Fleming, George T. ;

• Search DOE PAGES for author "Fleming, George T."
• Search DOE PAGES for ORCID "0000-0002-4987-7167"
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Gasbarro, Andrew D.; Howarth, Dean; Raben, Timothy G. ;

• Search DOE PAGES for author "Raben, Timothy G."
• Search DOE PAGES for ORCID "0000-0003-2681-4179"
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Tan, Chung-I; Weinberg, Evan S.

Publication Date:

2021-11-05

Research Org.:

Boston Univ., MA (United States)

Sponsoring Org.:

USDOE; Swiss National Science Foundation (SNSF)

OSTI Identifier:

1829176

Alternate Identifier(s):

OSTI ID: 1833383

Grant/Contract Number:  

SC0015845; SC0019061; 200021_175761

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 104 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS