arXiv subjects

A. A. Tseytlin

Publications and source records attributed to A. A. Tseytlin.

At least 127 records · Page 7Linked to original sources

arXiv2004

Semiclassical strings and AdS/CFT

We discuss AdS/CFT duality in the sector of ``semiclassical'' string states with large quantum numbers. We review the coherent-state effective action approach, in which similar 2d sigma model actions appear from the AdS_5 x S^5 string action and from the integrable spin chain Hamiltonian representing the N=4 super Yang-Mills dilatation operator. We consider mostly the leading-order terms in the energies/anomalous dimensions which match but comment also on higher-order corrections.

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arXiv2004

Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory

We review recent progress in checking AdS/CFT duality in the sector of ''semiclassical'' string states dual to ''long'' scalar operators of N=4 super Yang-Mills theory. In particular, we discuss the effective action approach, in which the same sigma model type action describing coherent states is shown to emerge from the AdS_5 x S^5 string action and from the spin chain Hamiltonian representing the SYM dilatation operator.

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arXiv2004

On one-loop correction to energy of spinning strings in S^5

We revisit the computation (hep-th/0306130) of 1-loop AdS_5 x S^5 superstring sigma model correction to energy of a closed circular string rotating in S^5. The string is spinning around its center of mass with two equal angular momenta J_2=J_3 and its center of mass angular momentum is J_1. We revise the argument in hep-th/0306130 that the 1-loop correction is suppressed by 1/J factor (J= J_1 + 2 J_2 is the total SO(6) spin) relative to the classical term in the energy and use numerical methods to compute the leading 1-loop coefficient. The corresponding gauge theory result is known (hep-th/0405055) only in the J_1=0 limit when the string solution becomes unstable and thus the 1-loop shift of the energy formally contains an imaginary part. While the comparison with gauge theory may not be well-defined in this case, our numerical string theory value of the 1-loop coefficient seems to disagree with the gauge theory one. A plausible explanation should be (as in hep-th/0405001) in the different order of limits taken on the gauge theory and the string theory sides of the AdS/CFT duality.

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arXiv2004

Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations

We consider AdS_5 x S^5 string states with several large angular momenta along AdS_5 and S^5 directions which are dual to single-trace Super-Yang-Mills (SYM) operators built out of chiral combinations of scalars and covariant derivatives. In particular, we focus on the SU(3) sector (with three spins in S^5) and the SL(2) sector (with one spin in AdS_5 and one in S^5), generalizing recent work hep-th/0311203 and hep-th/0403120 on the SU(2) sector with two spins in S^5. We show that, in the large spin limit and at the leading order in the effective coupling expansion, the string sigma model equations of motion reduce to matrix Landau-Lifshitz equations. We then demonstrate that the coherent-state expectation value of the one-loop SYM dilatation operator restricted to the corresponding sector of single trace operators is also effectively described by the same equations. This implies a universal leading order equivalence between string energies and SYM anomalous dimensions, as well as a matching of integrable structures. We also discuss the more general 5-spin sector and comment on SO(6) states dual to non-chiral scalar operators.

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arXiv2004

Towards the exact dilatation operator of N=4 super Yang-Mills theory

We investigate the structure of the dilatation operator D of planar N=4 SYM in the sector of single trace operators built out of two chiral combinations of the 6 scalars. Previous results at low orders in `t Hooft coupling λsuggest that D has the form of an SU(2) spin chain Hamiltonian with long range multiple spin interactions. Instead of the usual perturbative expansion in powers of λ, we split D into parts D^(n) according to the number n of independent pairwise interactions between spins at different sites. We determine the coefficients of spin-spin interaction terms in D^(1) by imposing the condition of regularity of a BMN-type scaling limit. For long spin chains, these coefficients turn out to be expressible in terms of hypergeometric functions of λ, which have regular expansions at both small and large values of λ. This suggest that anomalous dimensions of ``long'' operators in the two-scalar sector should generically scale as square root of λat large coupling, i.e. in the same way as energies of semiclassical states in dual AdS5 x S5 string theory. We speculate that D^(1) may be a Hamiltonian of a new integrable spin chain.

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arXiv2004

Quantizing three-spin string solution in AdS_5 x S^5

As was recently found in hep-th/0304255, there exists a simple non-supersymmetric classical solution describing a closed string rotating in S^5 and located at the center of AdS_5. It is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J' in the two other orthogonal rotation planes. The dual N=4 SYM operators should be scalar operators in SU(4) representations [0,J-J',2J'] or [J'-J,0,J'+J]. This solution is stable if J' > 3/2 J and for large J + 2 J' its classical energy admits an expansion in positive powers of g_eff = λ/(J + 2 J')^2: E= J + 2 J' + g_eff J' + ... . This suggests a possibility of a direct comparison with perturbative SYM results for the corresponding anomalous dimensions in the sector with g_eff << 1, by analogy with the BMN case. We conjecture that all quantum sigma model string corrections are then subleading at large J', so that the classical formula for the energy is effectively exact to all orders in λ. It could then be interpolated to weak coupling, representing a prediction for the anomalous dimensions on the SYM side. We test this conjecture by computing the 1-loop superstring sigma model correction to the classical energy.

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arXiv2004

Spinning strings and AdS/CFT duality

We review a special class of semiclassical string states in AdS_5 x S^5 which have a regular expansion of their energy in integer powers of the ratio of the square of string tension (`t Hooft coupling) and the square of large angular momentum in S^5. They allow one to quantitatively check the AdS/CFT duality in non-supersymmetric sector of states and also help to uncover the role of integrable structures on the two sides of the string theory -- gauge theory duality.

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arXiv2004

Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains

By considering AdS_5 x S^5 string states with large angular momenta in S^5 one is able to provide non-trivial quantitative checks of the AdS/CFT duality. A string rotating in S^5 with two angular momenta J_1,J_2 is dual to an operator in N=4 SYM theory whose conformal dimension can be computed by diagonalizing a (generalization of) spin 1/2 Heisenberg chain Hamiltonian. It was recently argued and verified to lowest order in a large J=J_1+J_2 expansion, that the Heisenberg chain can be described using a non-relativistic low energy effective 2-d action for a unit vector field n_i which exactly matches the corresponding large J limit of the classical AdS_5 x S^5 string action. In this paper we show that this agreement extends to the next order and develop a systematic procedure to compute higher orders in such large angular momentum expansion. This involves several non-trivial steps. On the string side, we need to choose a special gauge with a non-diagonal world-sheet metric which insures that the angular momentum is uniformly distributed along the string, as indeed is the case on the spin chain side. We need also to implement an order by order redefinition of the field n_i to get an action linear in the time derivative. On the spin chain side, it turns out to be crucial to include the effects of integrating out short wave-length modes. In this way we gain a better understanding of how (a subsector of) the string sigma model emerges from the dual gauge theory, allowing us to demonstrate the duality beyond comparing particular examples of states with large J.

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arXiv2004

On open superstring partition function in inhomogeneous rolling tachyon background

We consider open superstring partition function Z on the disc in time-dependent tachyon background T= f(x_i) e^{m x_0} where the profile function f depends on spatial coordinates. We compute Z to second order in derivatives of f and compare the result with some previously suggested effective actions depending only on the first derivatives of the tachyon field. We also compute the target-space stress-energy tensor in this background and demonstrate its conservation in the ``on-shell'' case of the linear profile f= f_0 + q_i x_i corresponding to a marginal perturbation. We comment on the role of the rolling tachyon with linear spatial profile in the decay of an unstable D-brane.

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arXiv2003

Precision Spectroscopy of AdS/CFT

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weights of the corresponding non-near-BPS operators in planar N=4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the `t Hooft coupling lambda. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in lambda. This one-loop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly non-trivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.

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arXiv2003

Spinning strings in AdS_5 x S^5 and integrable systems

We show that solitonic solutions of the classical string action on the AdS_5 x S^5 background that carry charges (spins) of the Cartan subalgebra of the global symmetry group can be classified in terms of periodic solutions of the Neumann integrable system. We derive equations which determine the energy of these solitons as a function of spins. In the limit of large spins J, the first subleading 1/J coefficient in the expansion of the string energy is expected to be non-renormalised to all orders in the inverse string tension expansion and thus can be directly compared to the 1-loop anomalous dimensions of the corresponding composite operators in N=4 super YM theory. We obtain a closed system of equations that determines this subleading coefficient and, therefore, the 1-loop anomalous dimensions of the dual SYM operators. We expect that an equivalent system of equations should follow from the thermodynamic limit of the algebraic Bethe ansatz for the SO(6) spin chain derived from SYM theory. We also identify a particular string solution whose classical energy exactly reproduces the one-loop anomalous dimension of a certain set of SYM operators with two independent R charges J_1, J_2.

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arXiv2003

Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors

We find the minimal energy solution describing a folded closed string located at the center of AdS_5 and rotating simultaneously in two planes in S^5 with two arbitrary SO(6) angular momenta J_1 and J_2. In the case when J_1=J_2=J' we observe the precise agreement between the leading coefficient in the large J' expansion of the energy of this solution and the minimal eigen-value of the 1-loop anomalous dimension matrix of the corresponding [J',0,J'] SYM operators obtained by Beisert, Minahan, Staudacher and Zarembo in hep-th/0306139. We find also perfect agreement between string and SYM results in cases of states with unequal spins J_1 and J_2 dual to [J_2,J_1-J_2,J_2] operators. This represents a remarkable quantitative test of the AdS/CFT duality in a non-supersymmetric (and non-near-BPS) sector.

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arXiv2003

Multi-spin string solutions in AdS_5 x S^5

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 the 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 + ł]^{1/2} with łbeing the string tension or `t Hooft coupling. We discuss interpolation of the E(J') relation to weak coupling by identifying the N=4 SYM 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 stability of these classical solutions under small perturbations and comment on several generalizations.

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arXiv2003

On semiclassical approximation and spinning string vertex operators in AdS_5 x S^5

Following earlier work by Polyakov and Gubser, Klebanov and Polyakov, we attempt to clarify the structure of vertex operators representing string states which have large (``semiclassical'') values of AdS energy (equal to 4-d dimension Δ) and angular momentum J in S^5 or spin S in AdS_5. We comment on the meaning of semiclassical limit in the context of α' perturbative expansion for the 2-d anomalous dimensions of the corresponding vertex operators. We consider in detail the leading-order 1-loop renormalization of these operators in AdS_5 x S^5 sigma model (ignoring fermionic contributions). We find new examples of operators for which, as in the case considered in hep-th/0110196, the 1-loop anomalous dimension can be made small by tuning quantum numbers. We also comment on a possibility of deriving the semiclassical relation between Δand J or S from the marginality condition for the vertex operators, using a stationary phase approximation in the path integral expression for their 2-point correlator on a complex plane.

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arXiv2002

Solvable model of strings in a time-dependent plane-wave background

We investigate a string model defined by a special plane-wave metric ds^2 = 2dudv - l(u) x^2 du^2 + dx^2 with l(u) = k/u^2 and k=const > 0. This metric is a Penrose limit of some cosmological, Dp-brane and fundamental string backgrounds. Remarkably, in Rosen coordinates the metric has a ``null cosmology'' interpretation with flat spatial sections and scale factor which is a power of the light-cone time u. We show that: (i) This spacetime is a Lorentzian homogeneous space. In particular, like Minkowski space, it admits a boost isometry in u,v. (ii) It is an exact solution of string theory when supplemented by a u-dependent dilaton such that its exponent (i.e. effective string coupling) goes to zero at u=infinity and at the singularity u=0, reducing back-reaction effects. (iii) The classical string equations in this background become linear in the light-cone gauge and can be solved explicitly in terms of Bessel's functions; thus the string model can be directly quantized. This allows one to address the issue of singularity at the string-theory level. We examine the propagation of first-quantized point-particle and string modes in this time-dependent background. Using certain analytic continuation prescription we argue that string propagation through the singularity can be smooth.

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arXiv2002

A class of exact pp-wave string models with interacting light-cone gauge actions

We find a general class of pp-wave string solutions with NS-NS $H_3$ or R-R $F_3$ field strengths, which are analogous to solutions with non-constant $F_5$ recently considered by Maldacena and Maoz (hep-th/0207284). We show that: (i) all pp-wave solutions supported by non-constant $H_3$ or $F_p$ fields are exact type II superstring solutions to all orders in $\a'$; (ii) the corresponding light-cone gauge Green-Schwarz actions are non-linear in bosons but always quadratic in fermions, and describe UV finite 2-d theories; (iii) the pp-wave backgrounds supported by non-constant $F_3$ field do not have, in contrast to their $F_5$-field counterparts, ``supernumerary'' supersymmetries and thus the associated light-cone GS actions do not possess 2-d supersymmetry. We consider a specific example where the pp-wave $F_3$ background is parametrized by an arbitrary holomorphic function of one complex bosonic coordinate. The corresponding GS action has the same bosonic part, similar Yukawa terms but twice as many interacting world-sheet fermions as the (2,2) supersymmetric model originating from the analogous $F_5$ background. We also discuss the structure of massless scalar vertex operators in the models related to N=2 super sine-Gordon and N=2 super Liouville theories.

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arXiv2002

Semiclassical quantization of superstrings: AdS_5 x S^5 and beyond

We discuss semiclassical quantization of closed superstrings in AdS_5 x S^5. We consider two basic examples: point-like string boosted along large circle of S^5 and folded string rotating in AdS_5. In the first case we clarify the general structure of the sigma model perturbation theory for the energy of string states beyond the leading 1-loop order (related to the plane-wave limit). In the second case we argue that the large spin limit of the expression for the ground-state energy (i.e. for the dimension of the corresponding minimal twist gauge theory operator) has the form S + f(λ) \ln S to all orders in α' ~ λ^{-1/2} expansion, in agreement with the AdS/CFT duality. We also suggest an extension of the semiclassical approach to near-conformal (near-AdS) cases on the example of the fractional D3-brane on conifold background. Expanded version of talks at the Third International Sakharov Conference on Physics, Moscow, June 24-29, 2002 and at Strings 2002, Cambridge, July 15-20,2002

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arXiv2002

Wilson loops in N=4 SYM theory: rotation in S5

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).

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