# 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 Φ^{4} 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:

- Publication Date:

- 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

## Citation Formats

```
Brower, Richard C., Fleming, George T., Gasbarro, Andrew D., Howarth, Dean, Raben, Timothy G., Tan, Chung-I, and Weinberg, Evan S. Radial lattice quantization of 3D ϕ 4 field theory. United States: N. p., 2021.
Web. doi:10.1103/PhysRevD.104.094502.
```

```
Brower, Richard C., Fleming, George T., Gasbarro, Andrew D., Howarth, Dean, Raben, Timothy G., Tan, Chung-I, & Weinberg, Evan S. Radial lattice quantization of 3D ϕ 4 field theory. United States. https://doi.org/10.1103/PhysRevD.104.094502
```

```
Brower, Richard C., Fleming, George T., Gasbarro, Andrew D., Howarth, Dean, Raben, Timothy G., Tan, Chung-I, and Weinberg, Evan S. Fri .
"Radial lattice quantization of 3D ϕ 4 field theory". United States. https://doi.org/10.1103/PhysRevD.104.094502.
```

```
@article{osti_1829176,
```

title = {Radial lattice quantization of 3D ϕ 4 field theory},

author = {Brower, Richard C. and Fleming, George T. and Gasbarro, Andrew D. and Howarth, Dean and Raben, Timothy G. and Tan, Chung-I and Weinberg, Evan S.},

abstractNote = {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.},

doi = {10.1103/PhysRevD.104.094502},

journal = {Physical Review D},

number = 9,

volume = 104,

place = {United States},

year = {2021},

month = {11}

}

https://doi.org/10.1103/PhysRevD.104.094502

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