Abstract
We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su(2|3) sector of mathcal{N} = 4 super Yang-Mills theory, have a bare dimension ∼ N and are a linear combination of restricted Schur polynomials with p ∼ O(1) long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problems maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of p giant graviton branes, which is a U(p) Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder.
Highlights
Our goal in this article is to test this expectation for the class of operators holographically dual to giant graviton branes [5,6,7]
For operators dual to giant gravitons [5], the Young diagram labels have a small number of long columns and for operators dual to dual giant gravitons [6, 7], the Young diagram labels have a small number of long rows [8,9,10]
The mixing problem is described using a basis labeled by a pair of Young diagrams R and r1 and a graph σ
Summary
We use two bases of operators in this study. A formula for matrix elements of the dilatation operator in the restricted Schur polynomial basis is the starting point for our study. The formula we obtain is exact, meaning that it does not use any of the simplifications of large N. Specializing to operators with bare dimension of order N , labeled by Young diagrams with order 1 long rows or columns, naturally leads to a second basis for this class of operators, known as the Gauss graph operators. Working in this basis allows us to exploit simplifications of large N.
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