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We study the semiclassical spectrum of bosonic string theory on AdS_3 x S^1 in the limit of large AdS angular momentum. At leading semiclassical order, this is a subsector of the IIB superstring on AdS_5 x S^5. The theory includes strings…

The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) expanded in large spin S have the asymptotics \gamma= f ln S + f_c + 1/S (f_11 ln S + f_10) + ..., where f (the universal scaling function or cusp anomaly),…

We consider circular strings rotating with equal spins S_1=S_2=S in two orthogonal planes in AdS_5 and suggest that they may be dual to "long" gauge theory operators built out of self-dual components of gauge field strength. As was found in…

We investigate the structure of the dilatation operator D of planar N=4 SYM in the sector of single trace operators built out of two chiral combinations of the 6 scalars. Previous results at low orders in `t Hooft coupling \lambda suggest…

This review is devoted to collecting some results on the high spin expansion of (minimal) anomalous dimension. Thanks to the recent rationale on integrability, planar ${\cal N}=4$ super Yang-Mills theory (or its…

We study operator mixing, due to planar one-loop corrections, for composite operators in D=4 supersymmetric theories. We present some N=1,2 Yang-Mills and Wess-Zumino models, in which the planar one-loop anomalous dimension matrix in the…

One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of…

It is shown that a supersymmetric and $\kappa$-symmetric D3-brane action on $AdS_5 \times S^5$ is mapped into itself by a duality transformaion, thereby verifying the $SL(2,Z)$ invariance of the D3-brane action in the $AdS_5 \times S^5$…

We analyze the folded spinning string in AdS_4 x P^3 with spin S in AdS_4 and angular momentum J in P^3. We calculate the one-loop correction to its energy in the scaling limit of both ln S and J large with their ratio kept fixed. This…

We study an angular dipole deformation of maximally supersymmetric Yang-Mills theory (SYM) that preserves its classical scale invariance. We show that two-point functions of suitable single trace operators, restricted to an invariant plane,…

It is shown that the large $N$ limit of SU(N) YM in $curved$ $m$-dim backgrounds can be subsumed by a higher $m+n$ dimensional gravitational theory which can be identified to an $m$-dim generally invariant gauge theory of diffs $N$, where…

Using the pure spinor formalism, a particular superstring scattering amplitude involving one closed string and $N$ open string vertex operators in $\mathrm{AdS}{}_5 \times \mathrm{S}^5$ is studied. It is shown that the tree-level amplitude…

We construct supersymmetric $AdS_5\times \Sigma$ solutions of $D=7$ gauged supergravity, where $\Sigma$ is a two-dimensional orbifold known as a spindle. These uplift on $S^4$ to solutions of $D=11$ supergravity which have orbifold…

Semiclassical spinning string states in AdS_5 are, in general, characterised by the three SO(2,4) conserved charges: the energy E and the two spins S_1 and S_2. We discuss several examples of explicit classical solutions for rigid closed…

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this…

We construct AdS$_5 \times \Sigma$ solutions of $D=7$ gauged supergravity where $\Sigma$ is a disc, also known as a half-spindle, and uplift them to $D=11$ supergravity. By computing the anomaly polynomial of the M5-brane theory…

We discuss semiclassical quantization of closed superstrings in AdS_5 x S^5. We consider two basic examples: point-like string boosted along large circle of S^5 and folded string rotating in AdS_5. In the first case we clarify the general…

We take the first steps to address via integrability the spectral problem of AdS/CFT dual pairs deformed by Groenewold-Moyal twists. In particular, we start by considering a twisted spin-chain that couples, through a Groenewold-Moyal twist…

We describe new solutions for open string moving in AdS_5 and ending in the boundary, namely dual to Wilson loops in N=4 SYM theory. First we introduce an ansatz for Euclidean curves whose shape contains an arbitrary function. They are BPS…

N=6 superconformal Chern-Simons theory with gauge group U(M)xU(N)} is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C4/Zk orbifold singularity. We show that, much like its regular counterpart…