## Compact conformal manifolds

## Abstract

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such manifolds are Kähler, and so the simplest possible non-trivial compact conformal manifold in this set of geometries is a complex one-dimensional projective space. We show that such a manifold is indeed realized and give a general prescription for constructing complex N-dimensional projective space conformal manifolds as certain small N = 2 → N = 1 breaking deformations of strongly interacting N = 2 SCFTs. In many cases, our prescription reduces the construction of such spaces to a study of the N = 2 chiral ring. We also give an algorithm for constructing more general compact spaces of SCFTs.

- Authors:

- Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy

- Publication Date:

- Research Org.:
- Rutgers Univ., Piscataway, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1454525

- Grant/Contract Number:
- SC0007897; SC0010008; SC0003883

- 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: 2015; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetric gauge theory; extended supersymmetry; renormalization group

### Citation Formats

```
Buican, Matthew, and Nishinaka, Takahiro. Compact conformal manifolds. United States: N. p., 2015.
Web. doi:10.1007/JHEP01(2015)112.
```

```
Buican, Matthew, & Nishinaka, Takahiro. Compact conformal manifolds. United States. doi:10.1007/JHEP01(2015)112.
```

```
Buican, Matthew, and Nishinaka, Takahiro. Wed .
"Compact conformal manifolds". United States. doi:10.1007/JHEP01(2015)112. https://www.osti.gov/servlets/purl/1454525.
```

```
@article{osti_1454525,
```

title = {Compact conformal manifolds},

author = {Buican, Matthew and Nishinaka, Takahiro},

abstractNote = {In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such manifolds are Kähler, and so the simplest possible non-trivial compact conformal manifold in this set of geometries is a complex one-dimensional projective space. We show that such a manifold is indeed realized and give a general prescription for constructing complex N-dimensional projective space conformal manifolds as certain small N = 2 → N = 1 breaking deformations of strongly interacting N = 2 SCFTs. In many cases, our prescription reduces the construction of such spaces to a study of the N = 2 chiral ring. We also give an algorithm for constructing more general compact spaces of SCFTs.},

doi = {10.1007/JHEP01(2015)112},

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

number = 1,

volume = 2015,

place = {United States},

year = {2015},

month = {1}

}

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