# Anomalies and bounds on charged operators

## Abstract

We study the implications of the ’t Hooft anomaly (i.e., obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is ${\mathbb{Z}}_{2}$. Using the modular bootstrap, universal bounds on ( $1+1$)-dimensional bosonic conformal field theories with an internal ${\mathbb{Z}}_{2}$ global symmetry are derived. The bootstrap bounds depend dramatically on the ’t Hooft anomaly. In particular, there is a universal upper bound on the lightest ${\mathbb{Z}}_{2}$ odd operator if the symmetry is anomalous, but there is no bound if the symmetry is nonanomalous. In the nonanomalous case, we find that the lightest ${\mathbb{Z}}_{2}$ odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a $U\left(1\right)$ global symmetry, and comment that there is no bound on the lightest $U\left(1\right)$ charged operator if the symmetry is nonanomalous.

- Authors:

- Publication Date:

- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)

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

- OSTI Identifier:
- 1545466

- Alternate Identifier(s):
- OSTI ID: 1595838

- Grant/Contract Number:
- SC0011632

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 2; 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

### Citation Formats

```
Lin, Ying-Hsuan, and Shao, Shu-Heng. Anomalies and bounds on charged operators. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.025013.
```

```
Lin, Ying-Hsuan, & Shao, Shu-Heng. Anomalies and bounds on charged operators. United States. doi:10.1103/PhysRevD.100.025013.
```

```
Lin, Ying-Hsuan, and Shao, Shu-Heng. Thu .
"Anomalies and bounds on charged operators". United States. doi:10.1103/PhysRevD.100.025013.
```

```
@article{osti_1545466,
```

title = {Anomalies and bounds on charged operators},

author = {Lin, Ying-Hsuan and Shao, Shu-Heng},

abstractNote = {We study the implications of the ’t Hooft anomaly (i.e., obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is Z2. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z2 global symmetry are derived. The bootstrap bounds depend dramatically on the ’t Hooft anomaly. In particular, there is a universal upper bound on the lightest Z2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is nonanomalous. In the nonanomalous case, we find that the lightest Z2 odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a U(1) global symmetry, and comment that there is no bound on the lightest U(1) charged operator if the symmetry is nonanomalous.},

doi = {10.1103/PhysRevD.100.025013},

journal = {Physical Review D},

number = 2,

volume = 100,

place = {United States},

year = {2019},

month = {7}

}

DOI: 10.1103/PhysRevD.100.025013

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