Strings In AdS Research Articles

Coordinate Bethe ansatz for the string S-matrix

We use the coordinate Bethe ansatz approach to derive the nested Bethe equations corresponding to the recently found S-matrix for strings in AdS5 × S5, compatible with centrally extended symmetry.

Strong-coupling expansion of cusp anomaly from quantum superstring

We consider the world surface in AdS5 that ends on two intersecting null lines at the boundary. The corresponding superstring partition function describes the expectation value of the Wilson line with a null cusp in dual large N maximally supersymmetric gauge theory and thus determines the cusp anomaly function f(l) of the gauge coupling l or the string tension √λ/2π. The first two coefficients in its strong-coupling or string inverse tension expansion were determined in hep-th/0210115 (a0 = 1) and in arXiv:0707.4254 (a1 = − 3 ln 2). Here we find that the 2-loop coefficient is a2 = −K where K is the Catalan's constant. This is in agreement (expected on the general grounds) with the previous results for f(l) as the coefficient of ln S term in the energy of the closed spinning string in AdS5. The string theory value for a2 is in agreement with the numerical result in hep-th/0611135 and the recent analytic result in arXiv:0708.3933 for the coefficients in strong-coupling Ssolution of the BES equation. We explicitly verify the cancellation of all 2-loop logarithmic divergences thus demonstrating the quantum consistency of the AdS5×S5 superstring action at this order. We also discuss the structure of the three and higher string loop corrections to the cusp anomaly function giving a 2d QFT diagrammatic interpretation to the result of arXiv:0708.3933 for the solution of the BES equation following from the Bethe ansatz prescription for the spectrum of the theory.

Spin chain from membrane and the Neumann-Rosochatius integrable system

We find membrane configurations in AdS{sub 4}xS{sup 7}, which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS{sub 5}xS{sup 5}. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.

Dual spikes—New spiky string solutions

We find a new class of spiky solutions for closed strings in flat, $AdS_3\subset AdS_5$ and $R\times S^2(\subset S^5)$ backgrounds. In the flat case the new solutions turn out to be T-dual configurations of spiky strings found by Kruczenski hep-th/0410226. In the case of solutions living in $AdS$, we make a semi classical analysis by taking the large angular momentum limit. The anomalous dimension for these dual spikes is similar to that for rotating and pulsating circular strings in AdS with angular momentum playing the role of the level number. This replaces the well known logarithmic dependence for spinning strings. For the dual spikes living on sphere we find that no large angular momentum limit exists.

Pure spinor strings in TsT deformed background

We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsT-transformed background are related to the isometry variables of the initial background in the universal way that is independent of the details of the background. We will argue that after redefinitions of pure spinors and the fermionic variables we can construct pure spinor action with manifest U(1) isometry. This fact implies that the pure spinor string in TsT-transformed background is described by pure spinor string in the original background where world-volume modes are subject to twisted boundary conditions. We will argue that these twisted boundary conditions generally prevent to prove the quantum conformal invariance of the pure spinor string in AdS_5 x S^5 background. We determine the conditions under which this quantum conformal invariance can be proved. We also determine the Lax pair for pure spinor strings in the TsT-transformed background.

Three-spin giant magnons inAdS5×S5

From the Polyakov string action using a conformal gauge we construct a three-spin giant magnon solution describing a long open string in AdS_5 \times S^5 which rotates both in two angular directions of S^5 and in one angular direction of AdS_5. Through the Virasoro constraints the string motion in AdS_5 takes an effect from the string configuration in S^5. The dispersion relation of the soliton solution is obtained as a superposition of two bound states of magnons. We show that there is a correspondence between a special giant magnon in AdS_2 and the sinh-Gordon soliton.

On AdS5×S5 string S-matrix

Recently two interesting conjectures about the string S-matrix on AdS5 × S 5 have been made. First, assuming the existence of a Hopf algebra symmetry Janik derived a functional equation for the dressing factor of the quantum string Bethe ansatz. Second, Hernandez and Lopez proposed an explicit form of 1/ √ λ correction to the dressing factor. In this Letter we show that in the strong coupling expansion Janik’s equation is solved by the dressing factor up to the order of its validity. This observation provides a strong evidence in favor of a conjectured Hopf algebra symmetry for strings in AdS5 × S 5 as well as the perturbative string S-matrix.

QUANTUM FLUCTUATIONS OF ROTATING STRINGS IN AdS5 × S5

We discuss quantum fluctuations of a class of rotating strings in AdS 5 × S 5. In particular, we develop a systematic method to compute the one-loop sigma-model effective actions in closed forms as expansions for large spins. As examples, we explicitly evaluate the leading terms for the constant radii strings in the SO (6) sector with two equal spins, the SU (2) sector, and the SL (2) sector. We also obtain the leading quantum corrections to the space–time energy for these sectors.

Exact expressions for quantum corrections to spinning strings

Abstract The one-loop worldsheet quantum corrections to the energy of spinning strings on R × S 3 within AdS 5 × S 5 are reexamined. The explicit expansion in the effective 't Hooft coupling λ ′ = λ / J 2 is rigorously derived. The expansion contains both analytic and non-analytic terms in λ ′ , as well as exponential corrections. Furthermore, we pin down the origin of the terms that are not captured by the quantum string Bethe ansatz, which only produces analytic terms in λ ′ . It is shown that the analytic terms arise from string fluctuations within the S 3 , whereas the non-analytic and exponential terms, which are not captured by the Bethe ansatz, originate from the fluctuations in all directions within the supersymmetric sigma model on AdS 5 × S 5 . We also comment on the case of spinning string in AdS 3 × S 1 .

Moduli Space of IIB Superstring and SUYMin AdS5×S5

This paper consists of two parts.In part I, we interpret the hidden symmetry of the moduli space ofIIB superstring on AdS5×S5 in terms of the chiralembedding in AdS5, which turns out to be the ℂℙ3conformal affine Toda model. We review how the position μ ofpoles in the Riemann–Hilbert formulation of dressingtransformation and the value of loop parameter μ in thevertex operator of affine algebra determine the moduli space ofthe soliton solutions, which describes the moduli space of theGreen–Schwarz superstring. We show also how this affine SU(4)symmetry affinizes the conformal symmetry in the twistor space, andhow a soliton string corresponds to a Robinson congruence withtwist and dilation spin coefficients μ of twistor.In part II, by extending the dressing symmetric action of IIB stringin AdS5×S5 to the D3 brane, we find a gaugedWZW action of Higgs Yang–Mills field including the 2-cocycle ofaxially anomaly. The left and right twistor structures of left andright α-planes glue into an ambitwistor. The symmetrygroup of Nahm equations is centrally extended to an affine group,thus we explain why the spectral curve is given by affine Toda.

Semiclassical strings in electric and magnetic field deformed AdS{sub 5}xS{sup 5} spacetimes

We first apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to the 11D M-theory with a stack N M2-branes to find the spacetime of a stack of N D2-branes with magnetic or electric flux in 10 D IIA string theory, after the Kaluza-Klein reduction. We then perform the T-duality to the spacetime to find the background of a stack of N D3-branes with magnetic or electric flux. In the near-horizon limit the background becomes the magnetic or electric field deformed AdS{sub 5}xS{sup 5}. We adopt an ansatz to find the classical string solution which is rotating in the deformed S{sup 5} with three angular momenta in the three rotation planes. The relations between the classical string energy and its angular momenta are found and results show that the external magnetic and electric fluxes will increase the string energy. Therefore, from the AdS/CFT point of view, the corrections of the anomalous dimensions of operators in the dual SYM theory will be positive. We also investigate the small fluctuations in these solutions and discuss the effects of magnetic and electric fields on the stability of these classical rotating string solutions. Finally, we find the possiblemore » solutions of string pulsating on the deformed spacetimes and show that the corrections to the anomalous dimensions of operators in the dual SYM theory are non-negative.« less

Non-relativistic superstrings: a new soluble sector of AdS5× S5

We find a new sector of string theory in AdS5 × S5 describing non-relativistic superstrings in that geometry. The worldsheet theory of non-relativistic strings in AdS5 × S5 is derived and shown to reduce to a supersymmetric free field theory in AdS2. Non-relativistic string theory provides a new calculable setting in which to study holography.

AdS strings with torsion: Noncomplex heterotic compactifications

Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric ${\mathrm{AdS}}_{4}$ compactifications on almost-Hermitian manifolds of $SU(3)$ structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly K\"ahler. We argue that all moduli are fixed, and we show that the K\"ahler potential and superpotential proposed in the literature yield the correct ${\mathrm{AdS}}_{4}$ radius. In the nearly K\"ahler case, we are able to solve the $H$ Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.

Quantum corrections to spinning strings inAdS5×S5and Bethe ansatz: a comparative study

We analyze quantum corrections to rigid spinning strings in AdS(5)xS(5). The one-loop worldsheet quantum correction to the string energy is compared to the finite-size correction from the quantum string Bethe ansatz. Expanding the summands of the string theory energy shift in the parameter \lambda/J^2 and subsequently resumming them yields a divergent result. However, upon zeta-function regularization this result agrees with the Bethe ansatz at the first three orders. We also perform an analogous computation in the limit of large winding number, which results in a disagreement with the string Bethe ansatz prediction. A similar mismatch is observed numerically. We comment on the possible origin of this discrepancy.

Wound and rotating strings inAdS5×S5

By using the non-diagonal uniform gauge for the Nambu-Goto string action we derive a gauge-fixed Hamiltonian of a square-root form for the closed string in AdS_5 x S^5 which is wound and rotating in an angular direction in S^5. From the Nambu-Goto string action using a non-diagonal gauge we construct a solution describing a wound string which rotates in the same angular direction as the winding direction. The relation between energy and angular momentum of the string solution is characterized by the winding number and the bending number, and becomes linear in the large angular momentum limit. The small angular momentum limit is compared with the strong coupling limit of the gauge-fixed Hamiltonian. We analyze a wound string solution which is rotating in the different angular direction from the winding direction.

PROBING THE 5TH DIMENSION WITH THE QCD STRING

A salient feature of String/Gauge duality is an extra 5th dimension. Here we study the effect of confining deformations of AdS5 and compute the spectrum of a string stretched between infinitely massive quarks and compare it with the quantum states of the QCD flux as determined by Kuti, Juge and Morningstar in lattice simulations. In the long flux tube limit the AdS string probes the metric near the IR cutoff of the 5th dimension with a spectrum approximated by a Nambu-Goto string in 4-d flat space, whereas at short distance the string moves to the UV region with a discrete spectrum for pure AdS5. We also review earlier results on glueballs states and the cross-over between hard and soft diffractive scattering that support this picture.

Gauge-string duality for superconformal deformations ofN= 4 Super Yang-Mills theory

We analyze in detail the relation between an exactly marginal deformation of N=4 SYM - the Leigh-Strassler or ``beta-deformation'' - and its string theory dual (recently constructed in hep-th/0502086) by comparing energies of semiclassical strings to anomalous dimensions of gauge-theory operators in the two-scalar sector. We stress the existence of integrable structures on the two sides of the duality. In particular, we argue that the integrability of strings in AdS_5 x S^5 implies the integrability of the deformed world sheet theory with real deformation parameter. We compare the fast string limit of the worldsheet action in the sector with two angular momenta with the continuum limit of the coherent state action of an anisotropic XXZ spin chain describing the one-loop anomalous dimensions of the corresponding operators and find a remarkable agreement for all values of the deformation parameter. We discuss some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe equations for small number of excitations and comment on higher loop properties of the dilatation operator. With the goal of going beyond the leading order in the 't Hooft expansion we derive the analog of the Bethe equations on the string-theory side, and show that they coincide with the thermodynamic limit of the Bethe equations for the spin chain. We also compute the 1/J corrections to the anomalous dimensions of operators with large R-charge (corresponding to strings with angular momentum J) and match them to the 1-loop corrections to the fast string energies. Our results suggest that the impressive agreement between the gauge theory and semiclassical strings in AdS_5 x S^5 is part of a larger picture underlying the gauge/gravity duality.

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

N=4 supersymmetric Yang-Mills operators carrying large charges are dual to semiclassical strings in AdS_5xS^5. The spectrum of anomalous dimensions of very large operators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.

Splitting strings and chains

AbstractWe review a study of the semiclassical decay of macroscopic spinning strings in AdS5 × S5 as well as its dual gauge theory description. The conservation of the infinite tower of commuting charges in the semiclassical string σ‐model description of the process suggests that the decay channel of maximal probability should preserve integrability in the gauge theory.

Matching quantum strings to quantum spins: One-loop vs. finite-size corrections

We compare quantum corrections to semiclassical spinning strings in AdS 5 × S 5 to one-loop anomalous dimensions in N = 4 supersymmetric gauge theory. The latter are computed using the reduced (Landau–Lifshitz) sigma model and with the help of the Bethe ansatz. The results of all three approaches are in remarkable agreement with each other. As a byproduct we establish the relationship between linear instabilities in the Landau–Lifshitz model and analyticity properties of the Bethe ansatz.