arXiv subjects

A. A. Tseytlin

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

At least 109 records · Page 6Linked to original sources

arXiv2006

Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions

Motivated by the desire to relate Bethe ansatz equations for anomalous dimensions found on the gauge theory side of the AdS/CFT correspondence to superstring theory on AdS_5 x S5 we explore a connection between the asymptotic S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum field theory. The latter generalizes the standard ``non-relativistic'' Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic Heisenberg spin chain and should be related to a limit of superstring effective action. We find the exact form of the quartic interaction terms in the generalized LL type action whose quantum S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders in the `t Hooft coupling an earlier computation of Klose and Zarembo of the S-matrix of the standard LL model. We also consider a generalization to the case when the spin chain S-matrix contains an extra ``string'' phase and determine the exact form of the LL 4-vertex corresponding to the low-energy limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the relation between the resulting ``non-relativistic'' non-local action and the second-derivative string sigma model. We comment on modifications introduced by strong-coupling corrections to the AFS phase. We mostly discuss the SU(2) sector but also present generalizations to the SL(2) and SU(1|1) sectors, confirming universality of the dressing phase contribution by matching the low-energy limit of the AFS-type spin chain S-matrix with tree-level string-theory S-matrix.

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arXiv2006

Slow-string limit and "antiferromagnetic" state in AdS/CFT

We discuss a slow-moving limit of a rigid circular equal-spin solution on R x S^3. We suggest that the solution with the winding number equal to the total spin approximates the quantum string state dual to the maximal-dimension ``antiferromagnetic'' state of the SU(2) spin chain on the gauge theory side. An expansion of the string action near this solution leads to a weakly coupled system of a sine-Gordon model and a free field. We show that a similar effective Hamiltonian appears in a certain continuum limit from the half-filled Hubbard model that was recently suggested to describe the all-order dilatation operator of the dual gauge theory in the SU(2) sector. We also discuss some other slow-string solutions with one spin component in AdS_5 and one in S^5.

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arXiv2006

On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory

We consider the highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory containing operators of the form tr(Z^{L-M} ψ^M) where Z is a complex scalar and ψis a component of gaugino. We show that this state corresponds to the operator tr(ψ^L) and can be viewed as an analogue of the antiferromagnetic state in the su(2) sector. We find perturbative expansions of the energy of this state in both weak and strong 't Hooft coupling regimes using asymptotic gauge theory Bethe ansatz equations. We also discuss a possible analog of this state in the conjectured string Bethe ansatz equations.

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arXiv2005

1/J^2 corrections to BMN energies from the quantum long range Landau-Lifshitz model

In a previous paper (hep-th/0509071), it was shown that quantum 1/J corrections to the BMN spectrum in an effective Landau-Lifshitz (LL) model match with the results from the one-loop gauge theory, provided one chooses an appropriate regularization. In this paper we continue this study for the conjectured Bethe ansatz for the long range spin chain representing perturbative planar N=4 Super Yang-Mills in the SU(2) sector, and the ``quantum string" Bethe ansatz for its string dual. The comparison is carried out for corrections to BMN energies up to 3rd order in the effective expansion parameter $\tl=λ/J^2$. After determining the ``gauge-theory'' LL action to order $\tl^3$, which is accomplished indirectly by fixing the coefficients in the LL action so that the energies of circular strings match with the energies found using the Bethe ansatz, we find perfect agreement. We interpret this as further support for an underlying integrability of the system. We then consider the ``string-theory'' LL action which is a limit of the classical string action representing fast string motion on an S^3 subspace of S^5 and compare the resulting $\tl^3/J^2$ corrections to the prediction of the ``string'' Bethe ansatz. As in the gauge case, we find precise matching. This indicates that the LL Hamiltonian supplemented with a normal ordering prescription and zeta-function regularization reproduces the full superstring result for the $1/J^2$ corrections, and also signifies that the string Bethe ansatz does describe the quantum BMN string spectrum to order $1/J^2$. We also comment on using the quantum LL approach to determine the non-analytic contributions in $λ$ that are behind the strong to weak coupling interpolation between the string and gauge results.

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arXiv2005

Effective action of beta-deformed N=4 SYM theory and AdS/CFT

We compute the one-loop effective action in \N=1 conformal SU(N) gauge theory which is an exactly marginal deformation of the \N=4 SYM theory. We consider an abelian background of constant \N = 1 gauge field and single chiral scalar. While for finite N the effective action depends non-trivially on the deformation parameter β, this dependence disappears in the large N limit if the parameter βis real. This conclusion matches the strong-coupling prediction coming from the form of a D3-brane probe action in the dual supergravity background: for the simplest choice of the D3-brane position the probe action happens to be the same as for a D3-brane in AdS_5 x S^5 placed parallel to the boundary of AdS_5. This suggests that in the real βdeformation case there exists a large N non-renormalization theorem for the 4-derivative term in the action.

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arXiv2005

On Quantum Corrections to Spinning Strings and Bethe Equations

Recently, it was demonstrated that one-loop energy shifts of spinning superstrings on AdS5xS5 agree with certain Bethe equations for quantum strings at small effective coupling. However, the string result required artificial regularization by zeta-function. Here we show that this matching is indeed correct up to fourth order in effective coupling; beyond, we find new contributions at odd powers. We show that these are reproduced by quantum corrections within the Bethe ansatz. They might also identify the "three-loop discrepancy" between string and gauge theory as an order-of-limits effect.

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arXiv2005

1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model

One way to relate semiclassical string states and dual gauge theory states is to show the equivalence between their low-energy effective 2d actions. The gauge theory effective action, which is represented by an effective Landau-Lifshitz (LL) model, was previously found to match with the string theory world-sheet action up to the first two orders in the effective parameter $\tildeλ ={λ/ J^2}$, where $λ$ is the `t Hooft coupling and $J$ is the total $R$-charge. Here we address the question if quantizing the effective LL action reproduces the subleading 1/J corrections to the spin chain energies as well as the quantum corrections to the string energies. We demonstrate that this is indeed the case provided one chooses an appropriate regularization of the effective LL theory. Expanding near the BPS vacuum, we show that the quantum LL action gives the same 1/J corrections to energies of BMN states as found previously on the gauge theory and string theory sides. We also compute the subleading $1/J^2$ corrections and show that these too match with corrections computed from the Bethe ansatz. We also compare the results from the LL action with a more direct computation from the spin chain. We repeat the same computation for the $β$-deformed LL action and find that the quantum LL result is again equal to the 1/J correction computed from the $β$-deformed Bethe ansatz equations. We also quantize the LL action near the rotating circular and folded string solutions, generalizing the known gauge/string results for 1/J corrections to the classical energies. We emphasize the simplicity of this effective field theory approach as compared to the full quantum string computations.

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arXiv2005

Gauge-string duality for superconformal deformations of N=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.

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arXiv2005

Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory

We consider a non-supersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS_5 x S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters gamma_i which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N=4 SYM theory, but with scalar and Yukawa interactions ``deformed'' by gamma_i-dependent phases. The special case of equal deformation parameters gamma_i=gamma corresponds to the N=1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal gamma_i this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective ``Landau-Lifshitz'' actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e. it allows one to capture the right vacuum states and the macroscopic spin wave sector of states of the spin chain in the continuum coherent state effective action.

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arXiv2005

R^4 terms in 11 dimensions and conformal anomaly of (2,0) theory

Using AdS_7/CFT_6 correspondence we discuss computation of a subleading O(N) term in the scale anomaly of (2,0) theory describing N coincident M5 branes. While the leading O(N^3) contribution to the anomaly is determined by the supergravity action, the O(N) contribution comes from a particular R^4 term (8d Euler density) in the 11-dimensional effective action. This R^4 term is argued to be part of the same superinvariant as the P-odd C_3 R^4 term known to produce O(N) contribution to the R-symmetry anomaly of (2,0) theory. The known results for R-anomaly suggest that the total scale anomaly extrapolated to N=1 should be the same as the anomaly of a single free (2,0) tensor multiplet. A proposed explanation of this agreement is that the coefficient 4N^3 in the anomaly (which was found previously to be also the ratio of the 2-point and 3-point graviton correlators in the (2,0) theory and in the free tensor multiplet theory) is shifted to 4N^3 -3N.

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arXiv2005

Super spin chain coherent state actions and $AdS_5 \times S^5$ superstring

We consider a generalization of the leading-order matching of coherent state actions for semiclassical states on the super Yang-Mills and the superstring sides of the AdS/CFT duality to sectors with fermions. In particular, we discuss the $SU(1|1)$ and $SU(2|3)$ sectors containing states with angular momentum $J$ in $S^5$ and spin in $AdS_5$. On the SYM side, we start with the dilatation operator in the $SU(2|3)$ sector having super spin chain Hamiltonian interpretation and derive the corresponding coherent state action which is quartic in fermions. This action has essentially the same ``Landau-Lifshitz'' form as the action in the bosonic SU(3) sector with the target space $CP^2$ replaced by the projective superspace $CP^{2|2}$. We then attempt to relate it to the corresponding truncation of the full $AdS_5 \times S^5$ superstring action written in a light-cone gauge where it has simple quartic fermionic structure. In particular, we find that part of the superstring action describing $SU(1|1)$ sector reduces to an action of a massive two-dimensional relativistic fermion, with the expansion in the effective coupling $λ/J^2$ being equivalent to a non-relativistic expansion.

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arXiv2005

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

We compare quantum corrections to semiclassical spinning strings in AdS(5)xS(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.

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arXiv2005

On Integrability of Classical SuperStrings in AdS_5 x S^5

We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both bosonic and fermionic fields.

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arXiv2005

Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector

We consider a circular string with spin $S$ in $AdS_5$ wrapped around big circle of $S^5$ and carrying also momentum $J$. The corresponding N=4 SYM operator belongs to the SL(2) sector, i.e. has tr$(D^S Z^J)+...$ structure. The leading large $J$ term in its 1-loop anomalous dimension can be computed using Bethe ansatz for the SL(2) spin chain and was previously found to match the leading term in the classical string energy. The string solution is stable at large $J$, and the Lagrangian for string fluctuations has constant coefficients, so that the 1-loop string correction to the energy $E_1$ is given simply by the sum of characteristic frequencies. Curiously, we find that the leading term in the zero-mode part of $E_1$ is the same as a 1/J correction to the one-loop anomalous dimension on the gauge theory (spin chain) side that was found in hep-th/0410105. However, the contribution of non-zero string modes does not vanish. We also discuss the ``fast string'' expansion of the classical string action which coincides with the coherent state action of the SL(2) spin chain at the first order in $ł$, and extend this expansion to higher orders clarifying the role of the $S^5$ winding number.

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arXiv2005

Semiclassical quantization of rotating superstring in AdS_5 x S^5

Motivated by recent proposals in hep-th/0202021 and hep-th/0204051 we develop semiclassical quantization of superstring in $AdS_5 x S^5$. We start with a classical solution describing string rotating in $AdS_5$ and boosted along large circle of $S^5$. The energy of the classical solution $E$ is a function of the spin $S$ and the momentum $J$ (R-charge) which interpolates between the limiting cases S=0 and J=0 considered previously. We derive the corresponding quadratic fluctuation action for bosonic and fermionic fields from the GS string action and compute the string 1-loop (large $λ= {R^4\over \a'^2}$) correction to the classical energy spectrum in the $(S,J)$ sector. We find that the 1-loop correction to the ground-state energy does not cancel for non-zero $S$. For large $S$ it scales as $\ln S$, i.e. as the classical term, with no higher powers of $\ln S$ appearing. This supports the conjecture made in hep-th/0204051 that the classical $E-S = a \ln S$ scaling can be interpolated to weak coupling to reproduce the corresponding operator anomalous dimension behaviour in gauge theory.

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arXiv2004

Complex geometry of conifolds and 5-brane wrapped on 2-sphere

We investigate solutions of type II supergravity which have the product R^4 x M^6 structure with non-compact M^6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N=1 supersymmetric NS5-brane wrapped on 2-sphere solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the Kaehler and parallel (3,0) forms of the corresponding M^6. In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of type II theory. We also demonstrate that the ordinary and fractional D3-brane solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields and a single 1-d action governing their radial evolution. We show that like the 3-branes on conifolds, the NS5-brane on 2-sphere background can be found as a solution of first order system following from a superpotential.

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arXiv2004

Spinning strings in AdS_5 x S^5: new integrable system relations

A general class of rotating closed string solutions in AdS_5 x 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 AdS_5 x 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 the two sides of the AdS/CFT duality. We find, in particular, new circular rotating string solutions with two AdS_5 and three 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 λ, suggesting that it can be matched onto the one-loop anomalous dimensions of the corresponding ``long'' operators on the SYM side of the AdS/CFT duality.

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arXiv2004

On gravitational couplings in D-brane action

We compute the two closed string graviton - two open string scalar scattering amplitude on the disc to show that there is no second-derivative curvature - scalar coupling term R X^2 in the low-energy effective action of a D-brane in curved space in type II superstring theory.

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