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We present the low-energy effective theory on long strings in quantum field theory, including a streamlined review of previous literature on the subject. Such long strings can appear in the form of solitonic strings, as in the 4d Abelian…

This dissertation reviews various aspects of the N=4 supersymmetric Yang--Mills theory in particular in relation with the AdS/CFT correspondence. The first two chapters are introductory. The first one contains a description of the general…

Motivated by desire to shed light on the strong coupling behaviour of anomalous dimensions of "short" gauge theory operators we consider the famous example of folded spinning string in AdS_5 in the limit of small semiclassical spin…

A topological sigma model based on the pure spinor formalism was recently proposed for the small radius limit of the AdS_5xS^5 superstring. Physical states in this model can be constructed by connecting holes on the worldsheet with Wilson…

We study the one-loop anomalous dimensions of the Super Yang-Mills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of…

We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3\times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant…

There is a class of single trace operators in ${\cal N}=4$ Yang-Mills theory which are related by the AdS/CFT correspondence to classical string solutions. Interesting examples of such solutions corresponding to periodic trajectories of the…

Anomalous dimension and higher conserved charges in the $sl(2)$ sector of ${\cal N}=4$ SYM for generic spin $s$ and twist $L$ are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under…

In this paper we investigate the finite-size properties of the spectrum of quantum spin chains with local spins taken to be the fundamental vector representation of the $OSp(n|2m)$ superalgebra.

We examine the AdS/CFT correspondence through a manifestly 5D supersymmetric formalism, corresponding to a 4D N=1 supersymmetric CFT. We find that the dimensions of scalar and fermionic component operators are simply related, and that there…

We consider $\alpha'$ corrections to four-point correlators of half-BPS operators in $\mathcal{N}=4$ super Yang-Mills theory in the supergravity limit. By demanding the correct behaviour in the flat space limit, we find that the leading…

We analyse semiclassical strings in AdS in the limit of one large spin. In this limit, classical string dynamics is described by a finite number of collective coordinates corresponding to spikes or cusps of the string. The semiclassical…

Long strings emerge in many Quantum Field Theories, for example as vortices in Abelian Higgs theories, or flux tubes in Yang-Mills theories. The actions of such objects can be expanded in the number of derivatives, around a long straight…

In the \beta-deformed N=4 supersymmetric SU(N) Yang-Mills theory we study the class of operators O_J = Tr(\Phi_i^J \Phi_k), i\neq k and compute their exact anomalous dimensions for N,J\to\infty. This leads to a prediction for the masses of…

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…

We present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher formalism,…

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…

We bootstrap loop corrections to AdS${}_5$ supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of $\mathcal{N}=4$ super Yang-Mills theory. In particular this yields much…

We present a self-contained review of the Plane-wave/super-Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large R-charge sector of N=4, D=4 superconformal U(N) gauge theory. This duality is…

We test the spectrum of string theory on AdS_5 x S^5 derived in hep-th/0305052 against that of single-trace gauge invariant operators in free N=4 super Yang-Mills theory. Masses of string excitations at critical tension are derived by…