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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 ${\cal N}=4$ super Yang-Mills theory, have a bare dimension $\sim N$ and are a linear combination of restricted Schur polynomials with $p\sim O(1)$ 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 problem 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., 34 pages

We study semiclassical string solutions that live on white regions of the LLM plane for a generic LLM geometry. These string excitations are labelled by conserved charges E, J and S and are thus holographically dual to operators in the SL(2) sector of N = 4 super-Yang Mills made up of covariant derivatives acting on complex scalar fields Z. On the other hand, the LLM geometry itself is dual to an operator consisting of O(N^2) Z-fields so that the operators dual to our solutions, containing both the stringy excitation and background, are non-planar. In an appropriate short string limit we argue that the string solution we find should be dual to a localised SL(2) excitation in the gauge theory language. This allows us to perform a non-trivial check of the recent proposal that the dynamics of localised excitations should be identical, up to a rescaling of the 't Hooft coupling, to the dynamics of those same excitations in the AdS5xS5 background, Comment: 10+3 pages

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants., 31 pages + appendices; v2 References added

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills theory. In this article we show that they can be extended to ABJM and ABJ theory. After making use of a novel identity which follows from character orthogonality, an integral representation of certain projection operators used to define Schur polynomials is given. This integral representation provides an effective description of the correlation functions of interest. The resulting effective descriptions have ${1\over N}$ as the loop counting parameter, strongly suggesting their relevance for holography., 1+22 pages, 3 Figures

A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi. This correlation function provides the holographic description of the absorption of a closed string by a giant graviton. The analysis has a natural interpretation in the framework of group representation theory, which admits a generalization to general Schur polynomials and restricted Schur polynomials. This generalizes the holographic description to any giant or dual giant gravitons which carry more than one angular momentum on the sphere. For a restricted Schur polynomial labeled by a column with $N$ boxes (dual to a maximal giant graviton) we find evidence in favor of integrability., 50 pages, 4 figures. v2: refs added

We consider operators in ${\cal N}=4$ super Yang-Mills theory dual to closed string states propagating on a class of LLM geometries. The LLM geometries we consider are specified by a boundary condition that is a set of black rings on the LLM plane. When projected to the LLM plane, the closed strings are polygons with all corners lying on the outer edge of a single ring. The large $N$ limit of correlators of these operators receives contributions from non-planar diagrams even for the leading large $N$ dynamics. Our interest in these fluctuations is because a previous weak coupling analysis argues that the net effect of summing the huge set of non-planar diagrams, is a simple rescaling of the 't Hooft coupling. We carry out some nontrivial checks of this proposal. Using the $su(2|2)^2$ symmetry we determine the two magnon $S$-matrix and demonstrate that it agrees, up to two loops, with a weak coupling computation performed in the CFT. We also compute the first finite size corrections to both the magnon and the dyonic magnon by constructing solutions to the Nambu-Goto action that carry finite angular momentum. These finite size computations constitute a strong coupling confirmation of the proposal., Comment: v2 matches published version

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve., Comment: Dedicated to the memory of Petr Kulish, 31 pages, 1 figure, v2: conformality and integrability of the boundary conditions are distinguished

We study structure constants of local operators inserted on the Wilson loop in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The results are interpreted as the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factors. This is consistent with a holographic description of the correlator as the cubic open string vertex, which consists of one hexagonal patch and three boundaries. We then conjecture that a similar expression should hold also at finite coupling., Comment: 38 pages; v3: JHEP published version

We compute both classical and quantum finite-size corrections at leading order in the strong coupling limit for the (dyonic) giant magnon in the Lunin–Maldacena background. Based on the exact S -matrix conjectured for the deformed theory, we generalize the Luscher formula to include twisted boundary conditions and show that the results match with those derived both by finite-size classical solutions of the giant magnon and by algebraic curve analysis.