# Nonlinearly realized conformal invariance in scale invariant field theories

## Abstract

I explore the implications of promoting nonconformal scale-invariant theories to conformal theories by nonlinearly realizing the missing symmetry. Properties of the associated Nambu-Goldstone mode imply that conformal invariance cannot be spontaneously broken to scale invariance in unitary theories and that, as well known, scale invariant unitary theories in two dimensions are also conformal. The promoted theories have only conformal primaries and no descendants. The (non) decoupling of the Nambu-Goldstone mode is explicitly shown in examples of scale invariant theories that are actually (not) conformal.

- Authors:

- Publication Date:

- Research Org.:
- Florida State Univ., Tallahassee, FL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)

- OSTI Identifier:
- 1501723

- Alternate Identifier(s):
- OSTI ID: 1601241

- Grant/Contract Number:
- SC0010102

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 99 Journal Issue: 6; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal field theory

### Citation Formats

```
Okui, Takemichi. Nonlinearly realized conformal invariance in scale invariant field theories. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.061701.
```

```
Okui, Takemichi. Nonlinearly realized conformal invariance in scale invariant field theories. United States. doi:10.1103/PhysRevD.99.061701.
```

```
Okui, Takemichi. Tue .
"Nonlinearly realized conformal invariance in scale invariant field theories". United States. doi:10.1103/PhysRevD.99.061701.
```

```
@article{osti_1501723,
```

title = {Nonlinearly realized conformal invariance in scale invariant field theories},

author = {Okui, Takemichi},

abstractNote = {I explore the implications of promoting nonconformal scale-invariant theories to conformal theories by nonlinearly realizing the missing symmetry. Properties of the associated Nambu-Goldstone mode imply that conformal invariance cannot be spontaneously broken to scale invariance in unitary theories and that, as well known, scale invariant unitary theories in two dimensions are also conformal. The promoted theories have only conformal primaries and no descendants. The (non) decoupling of the Nambu-Goldstone mode is explicitly shown in examples of scale invariant theories that are actually (not) conformal.},

doi = {10.1103/PhysRevD.99.061701},

journal = {Physical Review D},

number = 6,

volume = 99,

place = {United States},

year = {2019},

month = {3}

}

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DOI: 10.1103/PhysRevD.99.061701

DOI: 10.1103/PhysRevD.99.061701

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