Closed String Solutions Research Articles

Classical string solutions in non-relativistic AdS5 × S5: closed and twisted sectors

We find classical closed string solutions to the non-relativistic AdS5 × S5 string theory which are the analogue of the BMN and GKP solutions for the relativistic theory. We show that non-relativistic AdS5 × S5 string theory admits a orbifold symmetry which allows us to impose twisted boundary conditions. Among the solutions in the twisted sector, we find the one around which the semiclassical expansion in arXiv:2102.00008 takes place.

Stability analysis of classical string solutions and the dressing method

The dressing method is a technique to construct new solutions in non-linear sigma models under the provision of a seed solution. This is analogous to the use of autoBäcklund transformations for systems of the sine-Gordon type. In a recent work, this method was applied to the sigma model that describes string propagation on ℝ × S2, using as seeds the elliptic string solutions. Some of the new solutions that emerge reveal instabilities of their elliptic precursors [1]. The focus of the present work is the fruitful use of the dressing method in the study of the stability of closed string solutions. It establishes an equivalence between the dressing method and the conventional linear stability analysis. More importantly, this equivalence holds true in the presence of appropriate periodicity conditions that closed strings must obey. Our investigations point to the direction of the dressing method being a general tool for the study of the stability of classical string configurations in the diverse class of symmetric spacetimes.

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.

The generalized cusp in and more one-loop results from semiclassical strings

We evaluate the exact one-loop partition function for fundamental strings whose world surface ends on a cusp at the boundary of AdS4 and has a ‘jump’ in . This allows us to extract the stringy prediction for the ABJM-generalized cusp anomalous dimension ΓABJMcusp(ϕ, θ) up to NLO in sigma-model perturbation theory. With a similar analysis, we present the exact partition functions for folded closed string solutions moving in the AdS3 parts of and AdS3 × S3 × S3 × S1 backgrounds. Results are obtained applying to the string solutions relevant for the AdS4/CFT3 and AdS3/CFT2 correspondence the tools previously developed for their AdS5 × S5 counterparts.

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.

Kinky strings inAdS5×S5

We construct a family of closed string solutions with kinks in a subspace of AdS_5 x S^5 and study their properties. In certain limits these solutions become folded pulsating strings, although in general they are made of multiple pulsating rectangles. One unusual feature of these solutions is that their monodromy matrices are trivial, leading to vanishing quasi-momenta. Exact Backlund transformations of these solutions are found, again giving vanishing higher conserved charges. We also consider the fluctuation modes around these solutions as well as the semiclassical splitting of these strings.

Handbook on string decay

We explain simple semi-classical rules to estimate the lifetime of any given highly-excited quantum state of the string spectrum in flat spacetime. We discuss both the decays by splitting into two massive states and by massless emission. As an application, we study a solution describing a rotating and pulsating ellipse which becomes folded at an instant of time -- the ``squashing ellipse''. This string interpolates between the folded string with maximum angular momentum and the pulsating circular string. We explicitly compute the quantum decay rate for the corresponding quantum state, and verify the basic rules that we propose. Finally, we give a more general (4-parameter) family of closed string solutions representing rotating and pulsating elliptical strings.

Multi-spin string solutions in magnetic-flux deformedAdSn×Smspacetime

We perform the dimensional reduction of the spacetime of a stack of N D3-branes by the ``twist'' identification of a circle to obtain a new Melvin background. In the near-horizon limit the background becomes the magnetic-flux deformed $AdS_5 \times S^4$ or $AdS_4 \times S^5$ spacetime. After analyzing the classical closed string solutions with several angular momenta in different directions of the deformed spacetimes we obtain two string solutions. The first solution describes a circular closed string located at a fixed value of deformed $AdS_5$ radius while rotating simultaneously in two planes in deformed $AdS_5$ with equal spins $S$. The second solution describes a string rotating in deformed $S^5$ with two equal angular momenta $J$ in the two rotation planes. We investigate the small fluctuations therein and show that the magnetic fluxes have inclination to improve the stability of these classical string solutions.

Spinning strings inAdS5×S5:New integrable system relations

A general class of rotating closed string solutions in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ is shown to be described by a Neumann-Rosochatius one-dimensional integrable system. The latter represents an oscillator on a sphere or a hyperboloid with an additional ``centrifugal'' potential. We expect that the reduction of the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ sigma model to the Neumann-Rosochatius system should have further generalizations and should be useful for uncovering new relations between integrable structures on two sides of the AdS/conformal field theory (CFT) duality. We find, in particular, new circular rotating string solutions with two ${\mathrm{AdS}}_{5}$ and three ${\mathrm{S}}^{5}$ spins. As in other recently discussed examples, the leading large-spin correction to the classical energy turns out to be proportional to the square of the string tension or the 't Hooft coupling $\ensuremath{\lambda},$ suggesting that it can be matched onto the one-loop anomalous dimensions of the corresponding ``long'' operators on the super-Yang-Mills side of the AdS/CFT duality.

Open Spinning Strings

We find classical open string solutions in the $AdS_5\times S^5/\Zop_2$ orientifold with angular momenta along the five-sphere. The energy of these solutions has an expansion in integral powers of $\lambda$ with sigma-model corrections suppressed by inverse powers of $J$ - the total angular momentum. This gives a prediction for the exact anomalous dimensions of operators in the large $N$ limit of an ${\cal N}=2$ $Sp(N)$ Super-Yang-Mills theory with matter. We also find a simple map between open and closed string solutions. This gives a prediction for an all-loop planar relationship between the anomalous dimensions of single-trace and two-quark operators in the dual gauge theory.

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.

Generalized string theory mapping relations between gravity and gauge theory

A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang–Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang–Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, linking diagrams in gravity and Yang–Mills theory, as well as diagrams in pure effective Yang–Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open–closed string solutions, i.e., closed heterotic strings.

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.

Rotating and orbiting strings in the near-horizon brane backgrounds

Using the Schwarzschild-type coordinates in stead of the global ones we reconstruct the classical rotating closed string solutions in the AdS*5 x S*5 backgrounds. They are explicitly described by the Jacobi elliptic and trigonometrical functions of worldsheet coordinates. We study the orbiting closed string configurations in the near-horizon geometries of Dp, NS1 and NS5 branes, and derive the energy and spin of them, whose relation takes a simple form for short strings. Specially in the D5 and NS5 backgrounds we have a linear relation that the energy of the point-like string is proportional to the spin, which is associated with the spectrum of strings in the pp-wave geometries obtained by taking a special Penrose limit on the D5 and NS5 backgrounds.

Stationary solutions in 2 + 1-dimensional gravity with string sources

We make a systematic study of the stationary metric generated by string sources (i.e., one-dimensional matter distributions) in 2 + 1-dimensional gravity, extending the recent work of Deser and Jackiw. New open string solutions and closed string solutions with localized angular momentum are obtained and an interpretation, in terms of a string source, is given for the singularity of the Clément vacuum solution. Multi-string solutions are also discussed.