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In this paper, we investigate the circuit complexity of a quantum harmonic oscillator subjected to an external magnetic field. Utilizing the Nielsen approach within the thermofield dynamics (TFD) framework, we determine the complexity of thermofield double states as functions of time, temperature, and the external magnetic field. Our subsequent analysis reveals various features of this complexity. For instance, as temperature increases, the amplitude of complexity oscillations also rises, while at low temperatures, complexity stabilizes at a constant positive value. Furthermore, the magnetic field creates two distinct sectors: strong magnetic fields exhibit periodic complexity oscillations, whereas weak magnetic fields induce a beating effect. Finally, we confirm that the rate of complexity obeys the Lloyd bound., Comment: 18 pages, 5 figures

This study is aimed at providing a thorough analysis of the classical thermodynamic stability of black holes within the Anti-de Sitter (AdS) family. We utilize the Nambu bracket formalism to calculate local heat capacities and employ Sylvester's criterion in the mass-energy ensemble to determine both local and global thermodynamic stability regions. Emphasizing the crucial role of the cosmological constant, we establish the conditions necessary for the existence of thermodynamically stable black hole configurations. Our work highlights the applicability of classical thermodynamics in understanding black hole physics, while acknowledging the potential deviations that may impact the observables of the system beyond the classical level., Comment: Minor update: 1) Minor changes in the text, 2) Mising references were added

We revisit the classical thermodynamic stability of the standard black hole solutions by implementing 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. We show how weaker or incomplete conditions could lead to misleading or incorrect results for the thermodynamic stability of the system. We also stress the importance of finding all possible local heat capacities in order to fully describe the classical equilibrium picture of black holes. Finally, we thoroughly investigate the critical and phase transition curves and the limits of the classical analysis. 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: Minor update: 1. Conclusion revision, 2. Added missing references

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 Painlev\'e VI equation. Furthermore we have considered limits leading to a coalescence of singularities, which in turn transform the original Painlev\'e 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$^{\infty, q}$., Comment: 32 pages, three figures

The aim of this paper is to study the local and the global thermodynamic properties of the 3-dimensional rotating Gauss-Bonnet black hole. To this end we consider the conditions for local and global thermodynamic stability of the solution in a given ensemble of state quantities. Concerning the local analysis we found the regions of stability for every physical specific heat together with the existing Davies curves. Another central result is the generalization of the notion of global thermodynamic stability, known from the standard thermodynamics, to describe the global equilibrium of black holes. The new approach consists of applying specific Legendre transformation of the energy or the entropy to find the natural thermodynamic potential for the given ensemble of macro parameters. The global stability analysis, restricted to the week positivity conjecture is based on the properties of the new thermodynamic potential. The advantage of this method is that it allows one to chose different potentials, corresponding to different constraints to which the system may be subjected. Finally, we find it natural to impose global thermodynamic stability only where local one exists for the given black hole solution., Comment: 24 pages, 7 figures

The quest for extension of holographic correspondence to the case of finite temperature naturally includes Kerr-AdS black holes and their field theory duals. We probe the five-dimensional Kerr-AdS space time by pulsating strings. First we find particular pulsating string solutions and then semi-classically quantize the theory. For the string with large values of energy, we use the Bohr-Sommerfeld analysis to find the energy of the string as a function of a large quantum number. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which according to the holographic dictionary are related to anomalous dimensions of certain operators in the dual gauge theory. The interpretation of results from holographic point of view is not straightforward since the dual theory is at finite temperature. Nevertheless, near or at conformal point the expressions can be thought of as the dispersion relations of stationary states., Comment: 32 pp, 1 figure; v2: Sec.3 improved, Sec.4 recalculated for a general case, typos corrected, Appendix B included; v3: Sec.3 corrected, new figure of an effective potential added, typos corrected

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $\hat w$-operators. In this letter, we demonstrate that even more is true: a {\it single} $w$-constraint is sufficient to uniquely specify the partition functions provided one assumes that it is a power series in time-variables. This substitutes the previous specifications in terms of {\it two} requirements: either a string equation imposed on the KP/Toda $\tau$-function or a pair of Virasoro generators. This mysterious {\it single}-entry definition holds for a variety of theories, including Hermitian and complex matrix models, and also matrix models with external matrix: the unitary and cubic Kontsevich models. In these cases, it is equivalent to W-representation and is closely related to {\it super}\,integrability. However, a similar single equation that completely determines the partition function exists also in the case of the generalized Kontsevich model (GKM) with the potential of higher degree, when the constraint algebra is a larger $W$-algebra, and neither W-representation nor superintegrability are understood well enough., Comment: 11 pages

Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on the claim that the situation is improved when integrability is enhanced to super-integrability, i.e. to explicit formulas for Gaussian averages of characters. In this case, the Virasoro constraints are equivalent to simple recursive formulas, which have appropriate combinations of characters as their solutions. Moreover, one can easily separate dependence on the size of matrix, and deduce superintegrability from the Virasoro constraints. We describe one of the ways to do so for the Gaussian Hermitian matrix model. The result is a spectacularly elegant reformulation of Virasoro constraints as identities for the Schur functions evaluated at appropriate loci in the space of time-variables., Comment: 6 pages

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\"odinger 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\"odinger 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., Comment: Minor corrections

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

We find explicit solutions for giant magnons and spiky strings living on the Schr\"odinger $Schr_5 \times T^{1,1}$ 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., Comment: 30 pages

Recent progress in holographic correspondence uncovered remarkable relations between key characteristics of the theories on both sides of duality and certain integrable models. In this note we revisit the problem of the role of certain invariants in low-dimensional holography. As motivating example we consider first the entanglement entropy in 2d CFT and projective invariants. Next we consider higher projective invariants and suggest generalization to higher spin theories. Quadratic in invariants deformations is considered and conjectured to play role in low-dimensional higher spin holography., Comment: 23 pages, no figures

We study a holographic gauge theory dual to the D3/D5 intersection. We consider a pure gauge B-field flux through the internal two-sphere wrapped by the probe D5--brane, which corresponds to a non-commutative configuration of adjoint scalars. There is a domain wall separating the theory into regions with different ranks of the adjoint group. At zero temperature the theory is supersymmetric and at finite temperature there is a critical point of a second order phase transition. We study the corresponding critical exponents and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of -2/3., Comment: Updated to match the published version

According to AdS/CFT duality semi-classical strings in the Schr\"odinger spacetime is conjectured to be a holographic dual to dipole CFT. In this paper we consider pulsating strings in five-dimensional Schr\"odinger space times five-sphere. We have found classical string solutions pulsating entirely in the Schr\"odinger 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., Comment: 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

We derive the extended renormalized entanglement entropy (EREE) and the Fisher information metric in the case of closed bosonic strings in homogeneous plane wave background. Our investigations are conducted within the framework of Thermo Field Dynamics (TFD). The formalism is also illustrated on the example of some particular models in condensed matter physics and the non-equilibrium case for system with dissipations., Comment: 24 pages, 10 figures

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., Comment: 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

Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of AdS/CFT correspondence. On string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of large charges expansion of the dispersion relations for simple semiclassical strings in $AdS_4\times\mathbb{CP}^3$ background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three methods look different, power series expansions show their consistency., Comment: 24 pages, 2 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 present the general algorithm to establish the classical and quantum asymptotic symmetry algebra for non-AdS higher spin gravity and implement it for the specific example of spin-3 gravity in the non-principal embedding with Lobachevsky (H^2xR) boundary conditions. The asymptotic symmetry algebra for this example consists of a quantum W_3^2 (Polyakov-Bershadsky) and an affine u(1) algebra. We show that unitary representations of the quantum W_3^2 algebra exist only for two values of its central charge, the trivial c=0 "theory" and the simple c=1 theory., Comment: 23pp, v2: added Ref. [25], corrected typo in (5.4c)

Following the recent advances in the holographic calculation of n-point correlation functions with two "heavy" (with large quantum numbers) states at strong coupling, we extend these findings by computing specific four-point correlators of four heavy BMN operators in N=4 SYM., Comment: 11 pages, one figure, section removed, improvements made

Recently there has been progress on the calculation of three-point functions with two "heavy" operators via semiclassical methods. We extend this analysis to the case of the Lunin-Maldacena background, and examine the suggested procedure for several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual N=1 superconformal gauge theory, and recover an important relation connecting the dimensions of "heavy" states and the structure constants., Comment: 11 pages, no figures, incorrect subsection removed, typos fixed, references added and updated

Following the recent progress on the calculation of three-point correlators with two "heavy" (with large quantum numbers) and one "light" states at strong coupling, we compute the logarithmic divergent terms of leading bosonic quantum corrections to correlation functions with "heavy" operators corresponding to simple string solutions in AdS_5 x S^5. The "light" operator is chosen to be the dilaton. An important relation connecting the corrections to both the dimensions of "heavy" states, and the structure constants is recovered., Comment: 10 pages, no figures, improvements made

Recently there has been progress on the calculation of n-point correlation functions with two "heavy" (with large quantum numbers) states at strong coupling. We extend these findings by computing three-point functions corresponding to a folded three-spin semiclassical string with one angular momentum in AdS and two equal spins in the sphere. We recover previous results as limiting cases. Also, following a recent paper by Buchbinder and Tseytlin, we provide relevant four-point functions and consider some of their limits., Comment: 19 pages, no figures, minor changes

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 in AdS_5 x Y^{p,q} and AdS_5 x L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we find new solutions for this class in terms of Heun functions, and derive the particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539 [hep-th]. Unfortunately, Heun functions are still little studied, and we are not able to quantize the theory quasi-classically 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=1 superconformal field theory., Comment: 9 pages, talk given at the 2nd Int. Conference AMiTaNS, 21-26 June 2010, Sozopol, Bulgaria, organized by EAC (Euro-American Consortium) for Promoting AMiTaNS, to appear in the Proceedings of 2nd Int. Conference AMiTaNS

We study the class of pulsating strings in AdS_5 x T^{1,1}. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we semiclassically quantize the theory and obtain the first correction to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators in the dual N=1 superconformal gauge field theory., Comment: 12 pages, improvements made, references added

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., Comment: This paper has been withdrawn by the authors

In this paper we find giant magnon and single spike string solutions in a sector of the gamma-deformed conifold. We examine the dispersion relations and find a behavior analogous to the undeformed case. The transcendental functional relations between the conserved charges are shifted by certain gamma-dependent term. The latter is proportional to the total momentum and thus qualitatively different from known cases., Comment: 35 pages, no figures

In this paper we study the solitonic string solutions of magnon and single spike type in the beta-deformed AdS_4 x CP3 background. We find the dispersion relations which are supposed to give the anomalous dimension of the gauge theory operators., Comment: 11 pages, no figures, writings improved, 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., Comment: 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 use the reduction of the string dynamics on AdS_4 x CP^3 to the Neumann-Rosochatius integrable system. All constraints can be expressed simply in terms of a few parameters. We analyze the giant magnon and single spike solutions on R_t x CP^3 with two angular momenta in detail and find the energy-charge relations. The finite-size effects of the giant magnon and single spike solutions are analyzed., Comment: some improvements made, a section in appendix and references added;19 pages

Recently Maldacena and Swanson suggested a new limit of string theory on the $AdS_5\times S^5$ background, the so called near flat space limit. The resulting reduced theory interpolates between the pp-wave limit and giant magnon type string solutions. It was shown that the reduced model possess many features of the original theory. On the other hand, theories with less supersymmetry are of great importance for the string/gauge theory correspondence. In this paper we study the near flat limit reduction of string theory on the Maldacena-Nunez background, which is dual to $\N=1$ Yang-Mills theory. The reduced model interpolates between the pp-wave limit and a certain magnon type subsector of the theory. The similarity of the structures of the reduced model obtained here and that by Maldacena and Swanson indicates the possibility of existence of integrable subsectors of strings on the Maldacena-Nunez background., Comment: 1+23 pages, introduction improved and clarifying comments added, references added, results remain unchanged

We study rigid string solutions rotating in $AdS_5\times S^5$ background. For particular values of the parameters of the solutions we find multispin solutions corresponding to giant magnons and single spike strings. We present an analysis of the dispersion relations in the case of three spin solutions distributed only in $S^5$ and the case of one spin in $AdS_5$ and two spins in $S^5$. The possible relation of these string solutions to gauge theory operators and spin chains are briefly discussed., Comment: 45 pages, the presentation rearranged in 3 sections, results unchanged, references added, some typos corrected

Recently important classes of solitonic string solutions were obtained - giant magnons and single spikes. In previous study we showed the existence of giant magnon-like membrane solutions and studied their properties. In this paper we investigate classical rotating membranes representing analog of a specific class of string spiky solutions. Using the reduction to the Neumann-Rosochatius integrable system we find analog of the string single spike solutions. In contrast to the magnon-like solutions, this case is characterized with finite difference of energy and ``winding number'' and finite spins as well., Comment: LaTeX, 14 pages, no figures; v2: references added; v3: to appear in Nucl. Phys. B

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