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We revisit the thermodynamic stability of the standard black hole solutions by presenting the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria are quite generic and well-established in classical thermodynamics, but they have not been fully utilized in black hole physics. The global thermodynamic analysis is based on two equivalent criteria: the Hessian eigenvalue method in energy representation and the Sylvester criterion for positive definiteness of quadratic forms. The study of local thermodynamic stability is realized through the calculation of the admissible black hole heat capacities and their positiveness. The existence of critical points and phase transitions of the black hole is determined by the divergences of the corresponding heat capacities. This paper is the first in the line of intended works on thermodynamic stability of black holes in modified theories of gravity and holography., Comment: 27 pages, no figures, no tables

The aim of this paper is to study the effect of isomonodromic deformations of the evolution of scalar fields in Sasaki-Einstein spaces in the context of holography. Here we analyze the monodromy data of the general Heun equation, resulting from a scalar on Y$^{p,q}$, thus obtaining the corresponding Painlevé VI equation. Furthermore we have considered limits leading to a coalescence of singularities, which in turn transform the original Painlevé VI equation, to one of lower rank. The confluent limits we have considered are Y$^{p,p}$, T$^{1,1} / \mathbb{Z}_2$ and Y$^{\infty, q}$., 32 pages, three figures

The quest for extension of holographic correspondence to non-relativistic sectors naturally includes Schr\"odinger backgrounds and their field theory duals. In this paper we study the holography by probing the correspondence with pulsating strings. The case we consider is pulsating strings in five-dimensional Schr\"odinger space times five-torus $T^{1,1}$, which has as field theory dual a dipole CFT. First we find particular pulsating string solutions and then semi-classically quantize the theory. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT., Comment: Minor corrections, 18 pages, no figures, no tables

In this paper we study the Fisher information metric on the space of the coupling constants on both sides of the duality between non-relativistic dipole field theories and string theory in Schr��dinger spacetime. We consider the following setup. In the gauge theory side one can deform a given conformal field theory by a proper scalar operator and compute the quantum information metric via the two-point correlation function between two such operators. On the string side the deformation corresponds to a scalar field probing the background. In the large $N$ limit of the theory the probing can be done without backreaction on the original spacetime, thus one can construct a perturbative scheme for the calculation of the dual holographic Fisher information metric as shown by \cite{Trivella:2016brw}. Considering the asymptotic behaviour of the holographic Fisher information metric close to the boundary of the Schr��dinger spacetime we show that its divergence structure exactly matches its dual quantum counterpart up to the leading order, thus extending the holographic setup up to the non-relativistic case. One should note that the existence of other terms are not seen from the boundary theory to this level of approximation. Their behaviour near the boundary however, is pointing what kind of information from the boundary theory is missing to be able to reconstruct the bulk. Obviously more work is needed to refine and elucidate their meaning and interrelations in holographic setup., Minor corrections

We find explicit solutions for giant magnons and spiky strings living on the Schr��dinger $Schr_5 \times T^{1,1}$ and compute dispersion relations. The holographic dual field theory is conjectured to be a non-local dipole-deformed CFT at strong coupling. We find that the dependence between conserved charges in the dispersion relations is transcendental, which is quite different from the most symmetric case of spherical internal space. Keeping the squashing parameter $b$ general allows us to take some limits and to compare our results to known cases., 30 pages

According to AdS/CFT duality semi-classical strings in the Schr��dinger spacetime is conjectured to be a holographic dual to dipole CFT. In this paper we consider pulsating strings in five-dimensional Schr��dinger space times five-sphere. We have found classical string solutions pulsating entirely in the Schr��dinger part of the background. We quantize the theory semi-classically and obtain the wave function of the problem. We have found the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT., Minor corrections

We study the thermodynamic properties of warped AdS$_3$ black hole within the framework of thermodynamic information geometry. Our analysis focuses on finding the set of proper thermodynamic Riemannian metrics on the space of equilibrium states, together with the conditions for local and global thermodynamic stability. We use our findings to constrain the values of left and right central charges from the dual CFT theory and the parameters of the bulk gravitational theory., Comment: Minor corrections and improvements

One of the most important problems in any conformal field theory is the calculation of three-point functions of primary operators. In this paper we provide explicit examples of correlators with two scalar operators in $\,{\cal N}=4$ super-Yang--Mills theory at large $N$, corresponding to pulsating semiclassical strings in AdS$_5\times S^5$, and an operator with small quantum numbers at strong coupling., 12 pages, no figures, improvements made

In this paper we study D-brane scalar fluctuations in global Pilch-Warner background geometry. We consider configurations of the probe branes compatible with the kappa symmetry preserving condition and the brane classical equations of motion. The corresponding meson spectra, obtained by the fluctuations along the transverse brane directions, admit equidistant structure for the higher modes, but some of them show additional shifts in their ground states., Comment: 27 pages, no figures

There have been recent advances in the construction of algebraic curves for certain classes of string solutions in the context of the AdS/CFT correspondence. In this paper we obtain the Lax operators and associated spectral curves for circular and folded string solutions in $\,\textrm{AdS}_5\times S^5$. In addition, we provide an original approach for the reconstruction of string solutions in $\,S^3$ from their corresponding curves., Comment: 19 pages, no figures, references added

Higher-spin gravity in three dimensions is efficiently formulated as a Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N). The classical and quantum properties of the higher-spin theory depend crucially on the embedding into the full gauge algebra of the sl(2)+sl(2) factor associated with gravity. It has been argued previously that non-principal embeddings do not allow for a semi-classical limit (large values of the central charge) consistent with unitarity. In this work we show that it is possible to circumvent these conclusions. Based upon the Feigin-Semikhatov generalization of the Polyakov-Bershadsky algebra, we construct infinite families of unitary higher-spin gravity theories at certain rational values of the Chern-Simons level that allow arbitrarily large values of the central charge up to c = N/4 - 1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860., Comment: 20 pp in CQG style, 1 eps figure, v2: added labels in Fig. and 1 Ref

We study the class of pulsating strings on $AdS_5\times T^{1,1}$. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasi-classically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual ${\cal N}=1$ superconformal field theory., This paper has been withdrawn by the authors

Recently there has been progress on the computation of two- and three-point correlation functions with two "heavy" states via semiclassical methods. We extend this analysis to the case of AdS_4 x CP^3, and examine the suggested procedure for the case of several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual N=6 Chern-Simons gauge theory., Comment: 26 pages, no figures, references added

We study the class of pulsating strings on AdS_4 x CP3. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasi-classically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=6 Chern-Simons theory., references added

The non-linear nature of string theory on non-trivial backgrounds related to the AdS/CFT correspondence suggests to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit which describes point-like strings and the so called "near flat space" limit which connects two different sectors of string theory -- pp-waves and "giant magnons". Recently another example of AdS/CFT duality emerged - $AdS_4/CFT_3$, which suggests duality between $\mathcal N=6$ CS theory and superstring theory on $AdS_4\times \cp$. In this paper we study the "near flat space" limit of strings on the $AdS_4\times \cp$ background and discuss possible applications of the reduced theory., Comment: 20 pages, typos corrected, references added

We study the reduction of the (bosonic) string sigma model on $AdS_4\times\cp$ background. We give a brief presentation of the reduction procedure for $AdS$ part and apply explicitly the reduction scheme to $\cp$ part of the model. A brief discussion and directions for further study are presented., Comment: 19 pages, references added, some typos corrected

We study rigid string solutions rotating on the S^3 subspace of the beta-deformed AdS_5xS^5 background found by Lunin and Maldacena. For particular values of the parameters of the solutions we find the known giant magnon and single spike strings. We present a single spike string solution on the deformed S^3 and find how the deformation affects the dispersion relation. The possible relation of this string solution to spin chains and the connection of the solutions on the undeformed S^3 to the sine-Gordon model are briefly discussed., Comment: 20 pages, 2 figures; v2: typos corrected, references added

Some of the recent important developments in understanding string/ gauge dualities are based on the idea of highly symmetric motion of ``string solitons'' in $AdS_5\times S^5$ geometry originally suggested by Gubser, Klebanov and Polyakov. In this paper we study symmetric motion of short strings in the presence of antisymetric closed string B field. We compare the values of the energy and the spin in the case of non-vanishing B field with those obtained in the case of B=0. The presence of NS-NS antisymmetric field couples the fluctuation modes that indicates changes in the quantum corrections to the energy spectrum., Comment: 20 pages

We re-examine the recent proposal of Rastelli, Sen and Zwiebach on the tachyon fluctuation of the vacuum string field theory representing a D25 brane, originally considered by Hata and Kawano. We show that the tachyon state satisfies the linearized equations of motion on-shell in the strong sense thereby allowing us to calculate the ratio of energy density to the tension of the D-brane to be $E_c/T_{25}\simeq \pi^2/3[1/16(ln2)^3]\simeq 0.62$. Our proof relies on a careful handling of the limits ($n\to\infty$) involved in the conformal theory description of the sliver and tachyon states. We conjecture that the sliver state represents a single D25 brane., Comment: 10 pages

We study Witten's background independent open-string field theory in the presence of a constant B-field at one loop level. The Green's function and the partition function with a constant B-field are evaluated for an annulus., Comment: 10 pages, no figure, Latex

In the present paper we study SU(N)->S(U(N/2)xU(N/2)) symmetry breaking in N=4 SYM via AdS/CFT correspondence. We consider two stacks of N/2 parallel D3 branes separated by a distance 2\vec d. In this case there is mixing between the different l-wave dilatonic KK modes. We calculate certain the two point correlation functions in the dual gauge theory. Due to mode mixing, the diagonal correlation functions have 1/N conformal-like correction as well as deformation terms. The off-diagonal correlators are also non-vanishing and their leading order is 1/N. We discuss briefly the spectrum of the glueball exitations., 25 pages, more comments on two throat geometry, decoupling limit and correction terms, a few typos corrected, two references added; to appear in Phys.Rev. D

Integrable hierarchy based on the constrained Osp(2$\mid%2) connection is considered. The connection with 2D supergravity and some analogies with the W$_3^{(2)}$ case are given. It is shown that super Virasoro transformations are symmetries of tha hierarchy., Comment: 9pgs

In this paper we consider pulsating strings in warped $AdS_6\times S^4$ background, which is a vacuum solution of massive type {\bf IIA} superstring. The case of rotating strings in this background was considered in hep-th/0402202 and it was found that the results significantly differs from those considered in $AdS_5\times S^5$. Motivated by this results we study pulsating strings in the warped spherical part of the type {\bf IIA} geometry and compare the results with those obtained in hep-th/0209047, hep-th/0310188 and hep-th/0404012. We conclude with comments on our solutions and the obtained corrections to the energy, expanded to the leading order in lambda., 16 pages, references added

In this paper we investigate semiclassical rotating string configurations in the recently found Lunin-Maldacena background. This background is conjectured to be dual to the Leigh-Strassler beta-deformation of N=4 SYM and therefore a good laboratory for tests of the AdS/CFT correspondence beyond the well explored AdS(5)x S(5) case. We consider different multispin configurations of rotating strings by allowing the strings to move in both the AdS(5) and the deformed S(5) part of the Lunin-Maldacena background. For all of these configurations we compute the string energy in terms of the angular momenta and the string winding numbers and thus provide the possibility of comparing our results to the anomalous dimension of the corresponding dilatation operator., 16 pages, references added