Related papers: Quarter BPS classified by Brauer algebra
BPS coherent states closely resemble semiclassical states and they have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent…
We obtain all planar four-point correlators of half-BPS operators in $\mathcal{N}=4$ SYM up to five loops. The ansatz for the integrand is fixed partially by imposing light-cone OPE relations between different correlators. We then fix the…
We give a construction of general holomorphic quarter BPS operators in $ \mathcal{N}=4$ SYM at weak coupling with $U(N)$ gauge group at finite $N$. The construction employs the M\"obius inversion formula for set partitions, applied to…
We study the action of the dilatation operator on the basis of local operators constructed from the elements of the walled Brauer algebra, with non-planar corrections fully taken into account. We will see that the operator mixing can be…
We discuss the properties of quarter-BPS local operators in four dimensional ${\cal N}=1$ supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to…
Large $N$ but non-planar limits of ${\cal N}=4$ super Yang-Mills theory can be described using restricted Schur polynomials. Previous investigations demonstrate that the action of the one loop dilatation operator on restricted Schur…
In this article we study operators with a dimension $\Delta\sim O(N)$ and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are…
We continue the analysis of hep-th/0303060 in the one-loop sector and present the complete psu(2,2|4) dilatation operator of N=4 Super Yang-Mills theory. This operator generates the matrix of one-loop anomalous dimensions for all local…
A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of…
We obtain the planar correlation function of four half-BPS operators of arbitrary weights, up to three loops. Our method exploits only elementary properties of the integrand of the planar correlator, such as its symmetries and singularity…
We study the 1/4 BPS geometries corresponding to the 1/4 BPS operators of the dual gauge theory side, in ${\cal N}=4$ SYM. By analyzing asymptotic structure and flux integration of the geometries, we present a mapping between droplet…
Chiral primary operators annihilated by a quarter of the supercharges are constructed in the four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These quarter-BPS operators share many non-renormalization properties with the…
We calculate the four-point correlation function of half-BPS operators with weights 2, 3, 3, 4 in N=4 SYM to two-loop order. The OPE of this correlation function provides a nontrivial check of the integrability conjecture for a class of…
We compute the one loop anomalous dimensions of restricted Schur polynomials with a classical dimension \Delta\sim O(N). The operators that we consider are labeled by Young diagrams with two long columns or two long rows. Simple analytic…
We use hexagonalization to compute four-point correlation functions of long BPS operators with special R-charge polarizations. We perform the computation at weak coupling and show that at any loop order our correlators can be expressed in…
The four-point function of length-two half-BPS operators in $\mathcal{N}=4$ SYM receives non-planar corrections starting at four loops. Previous work relied on the analysis of symmetries and logarithmic divergences to fix the integrand up…
The calculation of a large family of four point functions of general BPS operators in N=4 SYM is reduced to the evaluation of colour contractions. For 1/2 BPS operators O_\Delta the explicit results at order g^4 for the function < O_n O_2…
We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry…
We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a…
The large N limit of the anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that have two columns (both long) so…