# SO(N) restricted Schur polynomials

## Abstract

We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d-1 dimensions and type II string theory defined on an AdS space in d-dimensions) dual in the form of type IIB string theory with AdS{sub 5}×RP{sup 5} geometry. With the aim of studying excited giant graviton dynamics, we construct an orthogonal basis for this sector of the gauge theory in this work. First, we demonstrate that the counting of states, as given by the partition function, and the counting of restricted Schur polynomials match by restricting to a particular class of Young diagram labels. We then give an explicit construction of these gauge invariant operators and evaluate their two-point function exactly. This paves the way to studying the spectral problem of these operators and their D-brane duals.

- Authors:

- Department of Physics and Centre for Theoretical Physics, National Institute for Theoretical Physics, University of the Witwatersrand (Wits), 2050 Johannesburg (South Africa)

- Publication Date:

- OSTI Identifier:
- 22403106

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFORMAL INVARIANCE; GAUGE INVARIANCE; PARTITION FUNCTIONS; POLYNOMIALS; STRING MODELS; STRING THEORY; YANG-MILLS THEORY; YOUNG DIAGRAM

### Citation Formats

```
Kemp, Garreth, E-mail: garreth.kemp@students.wits.ac.za.
```*SO(N) restricted Schur polynomials*. United States: N. p., 2015.
Web. doi:10.1063/1.4906904.

```
Kemp, Garreth, E-mail: garreth.kemp@students.wits.ac.za.
```*SO(N) restricted Schur polynomials*. United States. doi:10.1063/1.4906904.

```
Kemp, Garreth, E-mail: garreth.kemp@students.wits.ac.za. Sun .
"SO(N) restricted Schur polynomials". United States.
doi:10.1063/1.4906904.
```

```
@article{osti_22403106,
```

title = {SO(N) restricted Schur polynomials},

author = {Kemp, Garreth, E-mail: garreth.kemp@students.wits.ac.za},

abstractNote = {We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d-1 dimensions and type II string theory defined on an AdS space in d-dimensions) dual in the form of type IIB string theory with AdS{sub 5}×RP{sup 5} geometry. With the aim of studying excited giant graviton dynamics, we construct an orthogonal basis for this sector of the gauge theory in this work. First, we demonstrate that the counting of states, as given by the partition function, and the counting of restricted Schur polynomials match by restricting to a particular class of Young diagram labels. We then give an explicit construction of these gauge invariant operators and evaluate their two-point function exactly. This paves the way to studying the spectral problem of these operators and their D-brane duals.},

doi = {10.1063/1.4906904},

journal = {Journal of Mathematical Physics},

number = 2,

volume = 56,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}