SO(N) restricted Schur polynomials
Abstract
We focus on the 1/4BPS sector of free super YangMills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d1 dimensions and type II string theory defined on an AdS space in ddimensions) 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 twopoint function exactly. This paves the way to studying the spectral problem of these operators and their Dbrane 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; YANGMILLS THEORY; YOUNG DIAGRAM
Citation Formats
Kemp, Garreth, Email: garreth.kemp@students.wits.ac.za. SO(N) restricted Schur polynomials. United States: N. p., 2015.
Web. doi:10.1063/1.4906904.
Kemp, Garreth, Email: garreth.kemp@students.wits.ac.za. SO(N) restricted Schur polynomials. United States. doi:10.1063/1.4906904.
Kemp, Garreth, Email: garreth.kemp@students.wits.ac.za. 2015.
"SO(N) restricted Schur polynomials". United States.
doi:10.1063/1.4906904.
@article{osti_22403106,
title = {SO(N) restricted Schur polynomials},
author = {Kemp, Garreth, Email: garreth.kemp@students.wits.ac.za},
abstractNote = {We focus on the 1/4BPS sector of free super YangMills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d1 dimensions and type II string theory defined on an AdS space in ddimensions) 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 twopoint function exactly. This paves the way to studying the spectral problem of these operators and their Dbrane duals.},
doi = {10.1063/1.4906904},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = 2015,
month = 2
}

Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from N=4 SYM to type IIB string theory. In this paper we briefly expound the relationship between the restricted Schur polynomials and the operators forwarded by Brown, Heslop, and Ramgoolam. We then briefly examine the finite N counting of the restricted Schur polynomials.

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