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Abstract We construct generating functions for operators dual to systems of giant gravitons with open strings attached. These operators have a bare dimension of order N so that the usual methods used to solve the planar limit are not applicable. The generating functions are given as integrals over auxiliary variables, which implement symmetrization and antisymmetrization of the indices of the fields from which the operator is composed. Operators of a good scaling dimension (eigenstates of the dilatation operator) are known as Gauss graph operators. Our generating functions give a simple construction of the Gauss graph operators which were previously obtained using a Fourier transform on a double coset. The new description provides a natural starting point for a systematic 1 N $$ \frac{1}{N} $$ expansion for these operators as well as the action of the dilatation operator on them, in terms of a saddle point evaluation of their integral representation.

Abstract We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from circuits starting from scalar primary states. These results are nicely reproduced in terms of the geometry of coadjoint orbits of the conformal group. In contrast to the complexity geometry obtained from scalar primary states, the geometry is more complicated and the existence of conjugate points, signaling the saturation of complexity, remains open.

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 N $$ \mathcal{N} $$ = 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.

Abstract The state space of excited giant graviton brane systems is given by the Gauss graph operators. After restricting to the su(2|3) sector of the theory, we consider this state space. Our main result is the decomposition of this state space into irreducible representations of the su(2|2) ⋉ ℝ global symmetry. Excitations of the giant graviton branes are charged under a central extension of the global symmetry. The central extension generates gauge transformations so that the action of the central extension vanishes on physical states. Indeed, we explicitly demonstrate that the central charge is set to zero by the Gauss Law of the brane world volume gauge theory.

Abstract 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. Since this restricted Schur polynomial is a 1 2 $$ \frac{1}{2} $$ -BPS operator, this integrability is a corollary of the results of Jiang, Komatsu and Vescovi.

Abstract We consider operators in N=4 $$ \mathcal{N}=4 $$ 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.

Abstract We study three-point functions of operators on the 1/2 BPS Wilson loop in planar N $$ \mathcal{N} $$ = 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 SL2ℝ $$ \mathrm{S}\mathrm{L}\left(2,\mathbb{R}\right) $$ 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.

Abstract We study structure constants of local operators inserted on the Wilson loop in N=4 $$ \mathcal{N}=4 $$ super Yang-Mills theory. We conjecture the finite coupling expression of the structure constant which is interpreted as one hexagon with three mirror edges contracted by the boundary states. 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 check its validity at the weak coupling where the asymptotic expression reduces to the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factor. For this purpose, 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 result is nicely matched with our conjecture at the weak coupling regime.