# Displacement Operators and Constraints on Boundary Central Charges

## Abstract

Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. Moreover, we conjecture a relation between the α-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.

- Authors:

- Publication Date:

- Research Org.:
- San Francisco State Univ., San Francisco, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1416067

- Alternate Identifier(s):
- OSTI ID: 1501845

- Grant/Contract Number:
- SC0013682

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 120 Journal Issue: 2; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Herzog, Christopher, Huang, Kuo-Wei, and Jensen, Kristan. Displacement Operators and Constraints on Boundary Central Charges. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.120.021601.
```

```
Herzog, Christopher, Huang, Kuo-Wei, & Jensen, Kristan. Displacement Operators and Constraints on Boundary Central Charges. United States. doi:10.1103/PhysRevLett.120.021601.
```

```
Herzog, Christopher, Huang, Kuo-Wei, and Jensen, Kristan. Mon .
"Displacement Operators and Constraints on Boundary Central Charges". United States. doi:10.1103/PhysRevLett.120.021601.
```

```
@article{osti_1416067,
```

title = {Displacement Operators and Constraints on Boundary Central Charges},

author = {Herzog, Christopher and Huang, Kuo-Wei and Jensen, Kristan},

abstractNote = {Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. Moreover, we conjecture a relation between the α-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.},

doi = {10.1103/PhysRevLett.120.021601},

journal = {Physical Review Letters},

number = 2,

volume = 120,

place = {United States},

year = {2018},

month = {1}

}

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DOI: 10.1103/PhysRevLett.120.021601

DOI: 10.1103/PhysRevLett.120.021601

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Cited by: 7 works

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