## Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,\phantom{\rule{0ex}{0ex}}0)$ supergravity

## Abstract

We obtain new constraints on the anomaly coefficients of 6D $\mathcal{N}=(1,0)$ supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group G should be an element of 2H ^{4}(BG; Z) $$\otimes$$ Λ _{S} where Λ _{S} is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.

- Authors:

- Univ. of Geneva (Switzerland). Mathematics Section
- Rutgers Univ., Piscataway, NJ (United States). NHETC. Dept. of Physics and Astronomy

- Publication Date:

- Research Org.:
- Rutgers Univ., Piscataway, NJ (United States); Univ. of Geneva (Switzerland)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Swiss National Science Foundation (SNSF)

- OSTI Identifier:
- 1502365

- Grant/Contract Number:
- SC0010008; 152812; 165666

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; F-theory; supergravity models; superstring vacua; anomalies in field and string theories

### Citation Formats

```
Monnier, Samuel, Moore, Gregory W., and Park, Daniel S. Quantization of anomaly coefficients in 6D N = ( 1 , 0 ) supergravity. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)020.
```

```
Monnier, Samuel, Moore, Gregory W., & Park, Daniel S. Quantization of anomaly coefficients in 6D N = ( 1 , 0 ) supergravity. United States. doi:10.1007/jhep02(2018)020.
```

```
Monnier, Samuel, Moore, Gregory W., and Park, Daniel S. Mon .
"Quantization of anomaly coefficients in 6D N = ( 1 , 0 ) supergravity". United States. doi:10.1007/jhep02(2018)020. https://www.osti.gov/servlets/purl/1502365.
```

```
@article{osti_1502365,
```

title = {Quantization of anomaly coefficients in 6D N = ( 1 , 0 ) supergravity},

author = {Monnier, Samuel and Moore, Gregory W. and Park, Daniel S.},

abstractNote = {We obtain new constraints on the anomaly coefficients of 6D N = ( 1 , 0 ) supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group G should be an element of 2H4(BG; Z) $\otimes$ Λ S where Λ S is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.},

doi = {10.1007/jhep02(2018)020},

journal = {Journal of High Energy Physics (Online)},

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}

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