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We study local operators of U(N)xU(N) N=6 Chern-Simons-matter theory including a class of magnetic monopole operators. To take into account the interaction of monopoles and basic fields for large Chern-Simons level k, we consider the…
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…
We study spin models underlying the non-planar dynamics of ${\cal N}=4$ SYM gauge theory. In particular, we derive the non-local spin chain Hamiltonian generating dilatations in the gauge theory at leading order in $g_{\rm YM}^2 N$ but…
The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2,2|N) symmetry should possess universal integrability properties for different N. We provide further support for this…
The sl(2) sector of N=4 SYM theory has been much studied and the anomalous dimensions of those operators are well known. Nevertheless, many interesting operators are not included in this sector. We consider a class of twist operators beyond…
In this chapter of "Review of AdS/CFT Integrability" we introduce N=4 Super Yang-Mills. We discuss the global superalagebra PSU(2,2|4) and its action on gauge invariant operators. We then discuss the computation of the correlators of…
Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of…
The occurrence of the Askey-Wilson (AW) algebra in the $SU(2)$ Chern-Simons (CS) theory and in the Reshetikhin-Turaev (RT) link invariant construction with quantum algebra $U_q(\mathfrak{su}_2)$ is explored. Tangle diagrams with three…
Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N. In this paper, we compute the scaling dimensions of…
We study a sector of the 5d maximally supersymmetric Yang-Mills theory on $S^5$ consisting of $1/8$-BPS Wilson loop operators contained within a great $S^3$ inside $S^5$. We conjecture that these observables are described by a 3d Chern…
The discrete symmetry transformations of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed. Their bosonic limit is analyzed and new discrete symmetries of the modified GNLS hierarchy are derived. The explicit relations connecting…
We study four-dimensional gauge theories on oriented and non-spin spacetime manifolds. On such manifolds, each line operator arises only either as a boson or a fermion. Based on physical arguments, a method of systematically assigning spin…
We study conical defect geometries in the SL(N) Chern-Simons formulation of higher spin gauge theories in AdS_3. We argue that (for N\geq 4) there are special values of the deficit angle for which these geometries are actually smooth…
In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal…
We compute the two, three point function of the opearators in the spin zero multiplet of ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory at large $N$ and at all orders of 't Hooft coupling by solving the Schwinger-Dyson…
The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous)…
We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and…
We study issues concerning perturbative integrability of N=6 Chern-Simons theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics, we derive so called maximal-ranged interactions in the quantum dilatation generator,…
We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual…
By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin…