## Giant gravitons and the emergence of geometric limits in β-deformations of $$ \mathcal{N}=4 $$ SYM

## Abstract

We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1) ^{3} symmetry, known as β-deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g YM ^{2} N → ∞ limit. We argue that we can determine whether or not X is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take N → ∞ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of β are very important. When exp(iβ) is a root of unity, the space X is an orbifold. When exp(iβ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Lastly, if β is irrational, sporadic light states can be present.

- Authors:

- Univ. of California, Santa Barbara, CA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)

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

- OSTI Identifier:
- 1455052

- Grant/Contract Number:
- SC0011702; AC05-06OR23100

- 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; D-branes; AdS-CFT Correspondence; Gauge-gravity correspondence

### Citation Formats

```
Berenstein, David, and Dzienkowski, Eric. Giant gravitons and the emergence of geometric limits in β-deformations of $ \mathcal{N}=4 $ SYM. United States: N. p., 2015.
Web. doi:10.1007/JHEP01(2015)126.
```

```
Berenstein, David, & Dzienkowski, Eric. Giant gravitons and the emergence of geometric limits in β-deformations of $ \mathcal{N}=4 $ SYM. United States. doi:10.1007/JHEP01(2015)126.
```

```
Berenstein, David, and Dzienkowski, Eric. Fri .
"Giant gravitons and the emergence of geometric limits in β-deformations of $ \mathcal{N}=4 $ SYM". United States. doi:10.1007/JHEP01(2015)126. https://www.osti.gov/servlets/purl/1455052.
```

```
@article{osti_1455052,
```

title = {Giant gravitons and the emergence of geometric limits in β-deformations of $ \mathcal{N}=4 $ SYM},

author = {Berenstein, David and Dzienkowski, Eric},

abstractNote = {We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1)3 symmetry, known as β-deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g YM 2 N → ∞ limit. We argue that we can determine whether or not X is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take N → ∞ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of β are very important. When exp(iβ) is a root of unity, the space X is an orbifold. When exp(iβ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Lastly, if β is irrational, sporadic light states can be present.},

doi = {10.1007/JHEP01(2015)126},

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

number = 1,

volume = 2015,

place = {United States},

year = {2015},

month = {1}

}

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