Open String Solutions Research Articles

T-duality to scattering amplitude and Wilson loop in non-commutative super Yang-Mills theory

We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed AdS5×S5 spacetime, which corresponds to 4D mathcal{N}=4 non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to Killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual AdS5 × S5 spacetime but with a constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop) solution in the TsT-deformed AdS5 × S5 spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.

Conformal transformations and strings for an accelerating quark-antiquark pair in AdS 3

From a simple moving open string solution dual to a moving heavy quark with constant velocity in the Poincare AdS_3 spacetime, we construct an accerlerating open string solution dual to a heavy quark-antiquark pair accelerated in opposite directions by performing the three mappings such as the SL(2,R)_L x SL(2,R)_R isometry transformation, the special conformal transformation and the conformal SO(2,2) transformation. Using the string sigma model action we construct two open string solutions staying in two different regions whose dividing line is associated with the event horizon appeared on the string worldsheet and obtain the accelerating open string solution by gluing two such solutions.

Comparing double string theory actions

Aimed to a deeper comprehension of a manifestly T-dual invariant formulation of string theory, in this paper a detailed comparison between the non-covariant action proposed by Tseytlin and the covariant one proposed by Hull is done. These are obtained by making both the string coordinates and their duals explicitly appear, on the same foot, in the world-sheet action, so "doubling" the string coordinates along the compact dimensions. After a discussion of the nature of the constraints in both the models and the relative quantization, it results that the string coordinates and their duals behave like "non-commuting" phase space type coordinates but their expressions in terms of Fourier modes generate the oscillator algebra of the standard bosonic string formulation. A proof of the equivalence of the two formulations is given. Furthermore, open-string solutions are also discussed.

Spectral curve for open strings attached to the Y = 0 brane

The concept of spectral curve is generalized to open strings in AdS/CFT with integrability preserving boundary conditions. Our definition is based on the logarithms of the eigenvalues of the open monodromy matrix and makes possible to determine all the analytic, symmetry and asymptotic properties of the quasimomenta. We work out the details of the whole construction for the Y = 0 brane boundary condition. The quasimomenta of open circular strings are explicitly calculated. We use the asymptotic solutions of the Y -system and the boundary Bethe Ansatz equations to recover the spectral curve in the strong coupling scaling limit. Using the curve the quasiclassical fluctuations of some open string solutions are also studied.

BPS Wilson loop T-dual to spinning string in [formula omitted

We use the string sigma model action in AdS5×S5 to reconstruct the open string solution ending on the Wilson loop in S3×R parametrized by a geometric angle in S3 and an angle in flavor space. Under the interchange of the world sheet space and time coordinates and the T-duality transformation with the radial inversion, the static open string configuration associated with the BPS Wilson loop with two equal angle parameters becomes a long open spinning string configuration which is produced by taking the special limit of equal two frequencies for the folded spinning closed string with two spins in AdS5×S5.

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.

Generating string solutions in BTZ

Integrability of classical strings in the BTZ black hole enables the construction and study of classical string propagation in this background. We first apply the dressing method to obtain classical string solutions in the BTZ black hole. We dress time like geodesics in the BTZ black hole and obtain open string solutions which are pinned on the boundary at a single point and whose end points move on time like geodesics. These strings upon regularising their charge and spins have a dispersion relation similar to that of giant magnons. We then dress space like geodesics which start and end on the boundary of the BTZ black hole and obtain minimal surfaces which can penetrate the horizon of the black hole while being pinned at the boundary. Finally we embed the giant gluon solutions in the BTZ background in two different ways. They can be embedded as a spiral which contracts and expands touching the horizon or a spike which originates from the boundary and touches the horizon.

Thermodynamic Bethe ansatz equations for minimal surfaces in AdS 3

We study classical open string solutions with a null polygonal boundary in AdS 3 in relation to gluon scattering amplitudes in \( \mathcal{N} = 4 \) super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS n and generalized parafermions.

A note on string solutions inAdS3

We systematically search for classical open string solutions in AdS3 within the general class expressed by elliptic functions (i.e., the genus-one finite-gap solutions). By explicitly solving the reality and Virasoro conditions, we give a classification of the allowed solutions. When the elliptic modulus degenerates, we find a class of solutions with six null boundaries, among which two pairs are collinear. By adding the S1 sector, we also find four-cusp solutions with null boundaries expressed by the elliptic functions.

D-brane description of new open string solutions in [formula omitted

In this Letter we find D-brane descriptions of some of new open string solutions that were found in 0804.3438 [hep-th]. These D5-brane and D3-brane configurations give gravitational dual descriptions of Wilson loops in some particular representations.

Spiky strings, lightlike Wilson loops, and pp-wave anomaly

We consider rigid rotating closed strings with spikes in AdS5 dual to certain higher twist operators in N=4 SYM theory. In the limit of large spin when the spikes reach the boundary of AdS5, the solutions with different numbers of spikes are related by conformal transformations, implying that their energy is determined by the same function of the `t Hooft coupling f(lambda) that appears in the anomalous dimension of twist 2 operators or in the cusp anomaly. In the limit when the number of spikes goes to infinity, we find an equivalent description in terms of a string moving in an AdS pp-wave background. From the boundary theory point of view, the corresponding description is based on the gauge theory living in a 4d pp-wave space. Then, considering a charge moving at the speed of light, or a null Wilson line, we find that the integrated energy momentum tensor has a logarithmic UV divergence whose coefficient we call the "pp-wave anomaly". The AdS/CFT correspondence implies that, for N=4 SYM, this pp-wave anomaly should have the same value as the cusp anomaly. We verify this at lowest order in SYM perturbation theory. As a side result of our string theory analysis, we find new open string solutions in the Poincare patch of the standard AdS space which end on a light-like Wilson line and also in two parallel light-like Wilson lines at the boundary.

Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling

We compute the 1-loop correction to the effective action for the string solution in AdS5 × S5 dual to the circular Wilson loop. More generically, the method we use can be applied whenever the two dimensional spectral problem factorizes, to regularize and define the fluctuation determinants in terms of solutions of one-dimensional differential equations. A such it can be applied to non-homogeneous solutions both for open and closed strings and to various boundary conditions. In the case of the circular Wilson loop, we obtain, for the 1-loop partition function a result which up to a factor of two matches the expectation from the exact gauge theory computation. The discrepancy can be attributed to an overall constant in the string partition function coming from the normalization of zero modes, which we have not fixed.

Open spinning strings and AdS/dCFT duality

We consider open spinning string solutions on an AdS_4 x S^2-brane (D5-brane) in the bulk AdS_5 x S^5 background. By taking account of the breaking of SO(6)_R to SO(3)_H x SO(3)_V due to the presence of the AdS-brane, the open rotating string ansatz is discussed. We construct the elliptic folded/circular open string solutions in the SU(2) and the SL(2) sectors, so that they satisfy the appropriate boundary conditions. On the other hand, in the SU(2) sector of the gauge theory, we compute the matrix of anomalous dimension of the defect operator, which turns out to be the Hamiltonian of an open integrable spin chain. Then we consider the coordinate Bethe ansatz with arbitrary number of impurities, and compare the boundary condition of the Bethe wavefunction with that of the corresponding open string solution. We also discuss the Bethe ansatz for the open SL(2) spin chain with several supports from the string theory side. Then, in both SU(2) and SL(2) sectors, we analyze the Bethe equations in the thermodynamic limit and formulate the `doubling trick' on the Riemann surface associated with the gauge theory.

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.

Open cosmic strings in black hole space-times

We construct open cosmic string solutions in Schwarzschild black hole and non-dilatonic black p-brane backgrounds. These strings can be thought to stretch between two D-branes or between a D-brane and the horizon in curved space-time. We study small fluctuations around these solutions and discuss their basic properties.

Wilson loops inN=4super Yang-Mills theory: Rotation inS5

We study Wilson loops in N=4 SYM theory which are non-constant in the scalar (S5) directions and open string solutions associated with them in the context of AdS/CFT correspondence. An interplay between Minkowskian and Euclidean pictures turns out to be non-trivial for time-dependent Wilson loops. We find that in the S5-rotating case there appears to be no direct open-string duals for the Minkowskian Wilson loops, and their expectation values should be obtained by analytic continuation from the Euclidean-space results. In the Euclidean case, we determine the dependence of the ``quark - anti-quark'' potential on the rotation parameter, both at weak coupling (i.e. in the 1-loop perturbative SYM theory) and at strong coupling (i.e. in the classical string theory in AdS5 x S5).

Flowing from a noncommmutative (OM) five brane via its supergravity dual

The dual supergravity description of the flow between (2,0) five-brane theory and the noncommutative five-brane (OM) theory is examined at critical five-brane field strength. The self-duality of the field strength is shown to arise as a consequence of the supergravity solution. Open membrane solutions are examined in the background of the five-brane giving rise to an M analogue of the noncommutative open string (NCOS) solution.

Rotating string sources in three-dimensional gravity

The problem of finding the regular three-dimensional space-times, subject to the boundary condition g 00(∞) = 1, generated by a rotating string with tension is solved by a matrix method. According to the values of the string parameters, we obtain two classes of solutions. The solutions of the first class, which exist only if the string parameters are such that the string tension and centrifugal energy precisely balance, are topologically Euclidean. The second class of solutions, which exist only for negative or zero string mass densities, have an extra point at spatial infinity; in most instances, a satisfactory physical interpretation of these solutions is possible. We also briefly discuss stationary open string solutions.

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.