Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-06-04
JHEP 0811:061,2008
Physics
High Energy Physics
High Energy Physics - Theory
31 pages; v2: presentation improved
Scientific paper
10.1088/1126-6708/2008/11/061
Type IIB string theory on spacetimes that are asymptotically AdS$_5\times$S$^5$ can be defined using four dimensional ${\cal N}=4$ super Yang-Mills theory. Six of the dimensions of the string theory are holographically reconstructed in the Yang-Mills theory. In this article we study how these dimensions and local physics in these dimensions emerge. We reorganize the dynamics of the ${1\over 2}$ BPS sector of the field theory by rewriting it in terms of Schur polynomials. The Young diagram labeling of these polynomials can be viewed as a book keeping device which summarizes how the operator is constructed. We show that aspects of the geometry of the extra holographic dimensions are captured very naturally by the Young diagram. Gravitons which are localized at a specific position in the bulk correspond to boxes added at a specific location on the Young diagram.
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