A double coset ansatz for integrability in AdS/CFT

Understand

We give a proof that the expected counting of strings attached to giant graviton branes in AdS_5 x 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.