A double coset ansatz for integrability in AdS/CFT

A bstract We give a proof that the expected counting of strings attached to giant graviton branes in AdS 5  ×  S 5 , as constrained by the Gauss Law, matches the dimension spanned by the expected dual operators in the gauge theory. The counting of string-brane configurations is formulated as a graph...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2012; no. 6
Main Authors de Mello Koch, Robert, Ramgoolam, Sanjaye
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2012
Springer Nature B.V
Subjects
Branes
Classical and Quantum Gravitation
Elementary Particles
Fourier transforms
Gauge theory
Gravitons
Harmonic oscillators
High energy physics
Permutations
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Strings
AdS-CFT Correspondence
1/N Expansion
D-branes
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Summary:A bstract We give a proof that the expected counting of strings attached to giant graviton branes in AdS 5  ×  S 5 , as constrained by the Gauss Law, matches the dimension spanned by the expected dual operators in the gauge theory. The counting of string-brane configurations is formulated as a graph counting problem, which can be expressed as the number of points on a double coset involving permutation groups. Fourier transformation on the double coset suggests an ansatz for the diagonalization of the one-loop dilatation operator in this sector of strings attached to giant graviton branes. The ansatz agrees with and extends recent results which have found the dynamics of open string excitations of giants to be given by harmonic oscillators. We prove that it provides the conjectured diagonalization leading to harmonic oscillators.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP06(2012)083