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In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of…
We investigate (super) string theory on $AdS_3$ background based on an approach of free field realization. We demonstrate that this string theory can be reformulated as a string theory defined on a linear dilaton background along the…
We discuss the link between string backgrounds and the associated world-sheet CFTs. In the search for new backgrounds and CFTs, Penrose limits and Lie algebra contractions are important tools. The Nappi-Witten construction and the recently…
We find non-critical string backgrounds in five and eight dimensions, holographically related to four-dimensional conformal field theories with N=0 and N=1 supersymmetries. In the five-dimensional case we find an AdS_5 background metric for…
The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of…
It was recently shown that the CFT dual of string theory on ${\rm AdS}_3 \times {\rm S}^3 \times T^4$, the symmetric orbifold of $T^4$, contains a closed higher spin subsector. Via holography, this makes precise the sense in which…
We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on $AdS_5\times S^5$. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA…
We construct plane wave backgrounds with time-dependent profiles corresponding to Penrose limits of NS5-branes with transverse space symmetry group broken from SO(4) to SO(2)\times Z_N. We identify the corresponding exact theory as the…
String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string…
We study string propagation on $AdS_3$ times a compact space from an ``old fashioned'' worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the…
The recent developments towards the possible non-perturbative formulation of string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are discussed. In the first part, we give a critical review on the status of our present…
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…
Quantum non-local charges are central to the quantum integrability of a sigma-model. In this paper we study the quantum consistency and UV finiteness of non-local charges of string theory in AdS(5)xS(5). We use the pure spinor formalism. We…
We analyse the relation between two a priori quite different expansions of the string equations of motion and constraints in a general curved background, namely one based on the covariant Penrose-Fermi expansion of the metric G_{\mu\nu}…
We study semiclassical rotating strings in AdS/CFT backgrounds that exhibit both confinement and finite-size effects. The energy versus spin dispersion relation for short strings is the expected Regge trajectory behaviour, with the same…
We construct a new type of holographic correspondence between non-relativistic string theory in String Newton-Cartan AdS$_5\times$S$^5$ and Galilean Yang-Mills supplemented with 5 adjoint interacting scalar fields living on the 3+1…
A solvable irrelevant deformation of AdS$_3$/CFT$_2$ correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by…
Non-relativistic string theories promise to provide simpler theories of quantum gravity as well as tractable limits of the AdS/CFT correspondence. However, several apparently distinct non-relativistic string theories have been constructed.…
Based on the recently considered classical string configurations, in the framework of the semi-classical limit of the string/gauge theory correspondence, we describe a procedure for obtaining exact classical string solutions in general…
We study rigidly rotating strings in $\beta$-deformed $AdS_5\times S^5$ background with one spin along AdS$_5$ and two angular momenta along $S^5$. We find the spiky string solutions and present the dispersion relation among various charges…