String Solutions In AdS Research Articles

Considering the two spin and the two angular momenta string solutions in AdS5 × S5

In this paper, we consider two almost opposite sectors of actual string configuration ansätze in AdS5×S5, which anyway have almost the same features: The two spin solution, which has constant angles in S5 and the two angular momenta solution, which has constant “angels” in AdS5, however for the two angular momenta solution, we have to take the time coordinate from AdS5, thus there is a little asymmetry between the two string configurations in AdS5×S5.Without being autistic, there is around 69 equations between the similar equations in the two sectors, compare equations (34) and (104) and also compare equations (64) and (134). Again, without being autistic, the text after the equations in the two sectors, is almost precisely the same. In our notation, the difference between the two sectors is as follows; ρ↔θ, ϕ↔ψ, sinh⁡ρ↔sin⁡θ, yi↔xi, y↔x etc.The string configurations of this paper, are both solvable by the Neumann System. However, our setup in this paper is generally for the Neumann-Rosochatius System, which is also solvable, since we intend to generalize our results from the Neumann System to the Neumann-Rosochatius System and to several types of deformed Neumann-Rosochatius Systems.In the second part of this paper, which is independent of any string configurations in AdS5×S5 and concerns String Cosmology in D=10 dimensions. I will seriously argue that there was no Big Bang; I truly believe that the Universe has been there forever, see True Conclusions, Section 10.2

Precision calculation of 1/4-BPS Wilson loops in AdS5×S5

We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of "latitudes") in ${\cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5\times$S$^5$. Supersymmetric localization provides an exact result that, in the large 't Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the $ratio$ between the generic latitude and the maximal 1/2-BPS circle: Any measure-related ambiguity should simply cancel in this way. We use Gel'fand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: The difference is encoded into a precise "remainder function". We comment on the possible origin and resolution of this discordance.

On the algebraic curves for circular and folded strings in AdS5×S5

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 AdS. In addition, we provide an original approach for the reconstruction of string solutions in S3 from their corresponding curves.

Splitting of folded strings in AdS 4×CP 3

We study classically splitting of two kinds of folded string solutions in AdS_4*CP^3. Conserved charges of the produced fragments are computed for each case. We find interesting patterns among these conserved charges.

ONE-LOOP CORRECTION TO ENERGY OF SPINNING STRINGS IN AdS5×T1, 1

We consider circular spinning string solutions in AdS5×T1, 1 and calculate the quantum corrections to the energy at one-loop on worldsheet. The fluctuations are given as a set of harmonic oscillators and we calculate their normal mode frequency in closed form. The sum of frequency is equal to the one-loop string energy, which through AdS/CFT correspondence corresponds to the leading order correction of the conformal dimension for long operators in Klebanov–Witten conifold gauge field theory.

Quadratic corrections to three-point functions

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.

Semiclassical short strings in AdS5 × S 5

We present results for the one-loop correction to the energy of a class of string solutions in AdS_5 x S^5 in the short string limit. The computation is based on the observation that, as for rigid spinning string elliptic solutions, the fluctuation operators can be put into the single-gap Lame' form. Our computation reveals a remarkable universality of the form of the energy of short semiclassical strings. This may help to understand better the structure of the strong coupling expansion of the anomalous dimensions of dual gauge theory operators.

Review of AdS/CFT Integrability, Chapter II.1: Classical AdS 5 × S 5 String Solutions

We review basic examples of classical string solutions in AdS 5 × S 5. We concentrate on simplest rigid closed string solutions of circular or folded type described by integrable 1-d Neumann system but mention also various generalizations and related open-string solutions.

Exact computation of one-loop correction to the energy of pulsating strings in AdS5 × S5

In this paper, which is a sequel to Beccaria et al (2010 J. Phys. A: Math. Theor. 43 165402), we compute the one-loop correction to the energy of pulsating string solutions in AdS5 × S5. We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can also be put into the single-gap Lamé form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the ‘short-string’ limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of ‘small’ semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.

On the fermionic frequencies of circular strings

We revisit the semiclassical computation of the fluctuation spectrum around different circular string solutions in AdS5 × S5 and , starting from the Green–Schwarz action. It has been known that the results for these frequencies obtained from the algebraic curve and from the worldsheet computations sometimes do not agree. In particular, different methods give different results for the half-integer shifts in the mode numbers of the frequencies. We find that these discrepancies can be removed if one carefully takes into account the transition matrices in the spin bundle over the target space.

On the non-BPS string solutions in Sasaki-Einstein gauge/gravity duality

We present an extensive analysis on several string solutions in AdS 5 × Y p,q and find some interesting properties of their energy-spin relations. Their energy depends always on the parameter a(p, q) which characterizes these manifolds. The range of this parameter for the string solutions is constrained by the Sasaki-Einstein constraints that the solutions should satisfy. Hence some string solutions we find are not valid for the whole class of Y p,q manifolds. For some of our solutions, when the maximum allowed value of a(p, q) corresponds to the string approaching the poles of the squashed sphere in Y p,q , their energy at this limit approaches the BPS one. Thus certain non-BPS string solutions in the whole class of Sasaki-Einstein manifolds, can become BPS in particular manifolds. For the solutions with this property we point out that this behavior is independent of the string motion in the other directions on the manifold. We expect that in the field theory the corresponding generic operators to these semi-classical strings, become BPS at certain quivers.

Space-like minimal surfaces in AdS × S

We present a four parameter family of classical string solutions in AdS 3 ×S 3, which end along a light-like tetragon at the boundary of AdS 3 and carry angular momentum along two cycles on the sphere. The string surfaces are space-like and their projections on AdS 3 and on S 3 have constant mean curvature. The construction is based on the Pohlmeyer reduction of the related sigma model. After embedding in AdS 5 × S 5, we calculate the regularized area and analyze conserved charges. Comments on possible relations to scattering amplitudes are presented. We also sketch time-like versions of our solutions.

Conformal SO(2,4) transformations for the helical AdS string solution

By applying the conformal SO(2,4) transformations to the folded rotating string configuration with two spins given by a certain limit from the helical string solution in AdS_3 x S^1, we construct new string solutions whose energy-spin relations are characterized by the boost parameter. When two SO(2,4) transformations are performed with two boost parameters suitably chosen, the straight folded rotating string solution with one spin in AdS_3 is transformed in the long string limit into the long spiky string solution whose expression is given from the helical string solution in AdS_3 by making a limit that the modulus parameter becomes unity.

The [formula omitted] superstring quantum spectrum from the algebraic curve

We propose a method for computing the energy level spacing around classical string solutions in AdS 5 × S 5 . This method is based on the integrable structure of the string and can be applied to an arbitrary classical configuration. Our approach treats in equal footing the bosonic and fermionic excitations and provides an unambiguous prescription for the labeling of the fluctuation frequencies. Finally we revisit the computation of these frequencies for the SU ( 2 ) and SL ( 2 ) circular strings and compare our results to the existing ones.

Precision test of AdS/CFT in Lunin-Maldacena background

We obtain the solutions and explicitly calculate the energy for a class of two-spin semiclassical string states in the Lunin-Maldacena background. These configurations are \beta-deformed versions of the folded string solutions in AdS_{5}\times S^{5} background. They correspond to certain single trace operators in the \mathcal{N}=1 superconformal \beta deformation of \mathcal{N}=4 Yang-Mills. We calculate the one loop anomalous dimension for the dual single trace operator from the associated twisted spin chain with a general two-cut distribution of Bethe roots. Our results show a striking match between the two calculations. We demonstrate the natural identification of parameters on the two sides of the analysis, and explain the significance of the Virasoro constraint associated with the winding motion of semiclassical strings from the perspective of the spin chain solution.

Folded Three-Spin String Solutions inAdS5 S5

We construct a spinning closed string solution in AdS_5 x S^5 which is folded in the radial direction and has two equal spins in AdS_5 and a spin in S^5. The energy expression of the three-spin solution specified by the folding and winding numbers for the small S^5 spin shows a logarithmic behavior and a one-third power behavior of the large total AdS_5 spin, in the long string and in the short string located near the boundary of AdS_5 respectively. It exhibits the non-regular expansion in the 't Hooft coupling constant, while it takes the regular one when the S^5 spin becomes large.

Spinning and rotating strings forN=1 SYM theory and brane constructions

We obtain spinning and rotating closed string solutions in AdS5 × T1,1 background, and show how these solutions can be mapped onto rotating closed strings embedded in configurations of intersecting branes in type IIA string theory. Then, we discuss spinning closed string solutions in the UV limit of the Klebanov-Tseytlin background, and also properties of classical solutions in the related intersecting brane constructions in the UV limit. We comment on extensions of this analysis to the deformed conifold background, and in the corresponding intersecting brane construction, as well as its relation to the deep IR limit of the Klebanov-Strassler solution. We briefly discuss on the relation between type IIA brane constructions and their related M-theory descriptions, and how solitonic solutions are related in both descriptions.

Multi-spin string solutions in AdS5× S5

Motivated by attempts to extend AdS/CFT duality to non-BPS states we consider classical closed string solutions with several angular momenta in different directions of AdS 5 and S 5. We find a novel solution describing a circular closed string located at a fixed value of AdS 5 radius while rotating simultaneously in two planes in AdS 5 with equal spins S. This solution is a direct generalization of a two-spin flat-space solution where the string rotates in two orthogonal planes while always lying on a 3-sphere. Similar solution exists for a string rotating in S 5: it is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J 2= J 3= J′ in the two rotation planes. The remarkably simple case is of J=0 where the energy depends on J′ as E= (2J′) 2+λ ( λ is the string tension or 't Hooft coupling). We discuss interpolation of the E( J′) formula to weak coupling by identifying the gauge theory operator that should be dual to the corresponding semiclassical string state and utilizing existing results for its perturbative anomalous dimension. This opens up a possibility of studying AdS/CFT duality in this new non-BPS sector. We also investigate small fluctuations and stability of these classical solutions and comment on several generalizations.