Robert de Mello Koch

Giant gravitons - with strings attached (I)

In this article, the free field theory limit of operators dual to giant gravitons with open strings attached, are studied. We introduce a graphical notation, which employs Young diagrams, for these operators. The computation of two point correlation functions is reduced to the application of three simple rules, written as graphical operations performed on the Young diagram labels of the operators. Using this technology, we have studied gravitational radiation by giant gravitons and bound states of giant gravitons, transitions between excited giant graviton states and joining of open strings attached to the giant.

AdS 4 / CFT 3 construction from collective fields

We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the O(N) vector model in terms of canonical collective fields. In null plane quantization an exact map is established between the two spaces. The coordinates of the AdS_4 space-time are generated from the collective coordinates of the bi-local field. This, in the light cone gauge, provides an exact one to one reconstruction of bulk AdS_4 space-time and higher-spin fields.

Giant graviton oscillators

We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in

Giant graviton correlators from dual SU(N) super Yang-Mills theory

\mathcal{N} = 4

A double coset ansatz for integrability in AdS/CFT

super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.

Geometries from Young diagrams

Certain correlation functions are computed exactly in the zero coupling limit of = 4 super Yang-Mills theory with gauge group SU(N). A set of linearly independent operators that are in one-to-one correspondence with the half-BPS representations of the SU(N) gauge theory is given. These results are used to study giant gravitons in the dual AdS5 × S5 string theory. In addition, for the U(N) gauge theory, we explain how to systematically identify contributions coming from the boundary degrees of freedom.

Surprisingly simple spectra

A bstractWe give a proof that the expected counting of strings attached to giant graviton branes in AdS5 × S5, 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.

Emergent three-brane lattices

Type IIB string theory on spacetimes that are asymptotically AdS5 ? S5 can be defined using four dimensional = 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 ? 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.

From large N nonplanar anomalous dimensions to open spring theory

The large N limit of the anomalous dimensions of operators in

Deformed PP-waves from the Lunin-Maldacena background

\mathcal{N} = 4