Semiclassical String Research Articles

Semiclassical strings in marginally deformed toric AdS/CFT

We study string solutions in the beta-deformed Sasaki-Einstein gauge/gravity dualities. We find that the BPS point-like strings move in the submanifolds where the two U(1) circles shrink to zero size. In the corresponding T^3 fibration description, the strings live on the edges of the polyhedron, where the T^3 fibration degenerates to T^1. Moreover, we find that for each deformed Sasaki-Einstein manifold the BPS string solutions exist only for particular values of the deformation parameter. Our results imply that in the dual field theory the corresponding BPS operators exist only for these particular values of the deformation parameter we find. We also examine the non-BPS strings, derive their dispersion relations and compare them with the undeformed ones. Finally, we comment on the range of the validity of our solutions and their dependence on the deformation parameter.

On strong-coupling correlation functions of circular Wilson loops and local operators

Motivated by the problem of understanding 3-point correlation functions of gauge-invariant operators in super Yang–Mills theory we consider correlators involving Wilson loops and a ‘light’ operator with fixed quantum numbers. At leading order in the strong-coupling expansion such correlators are given by the ‘light’ vertex operator evaluated on a semiclassical string world surface ending on the corresponding loops at the boundary of AdS5 × S5. We study in detail the example of a correlator of two concentric circular Wilson loops and a dilaton vertex operator. The resulting expression is given by an integral of combinations of elliptic functions and can be computed analytically in some special limits. We also consider a generalization of the minimal surface ending on two circles to the case of non-zero angular momentum J in S5 and discuss a special limit when one of the Wilson loops is effectively replaced by a ‘heavy’ operator with charge J.

THREE- AND FOUR-POINT CORRELATORS OF OPERATORS DUAL TO FOLDED STRING SOLUTIONS IN AdS5 × S5

Recently there has been progress on the calculation of n-point correlation functions with two "heavy" (with large quantum numbers) states at strong coupling. We extend these findings by computing three-point functions corresponding to a folded three-spin semiclassical string with one angular momentum in AdS and two equal spins in the sphere. We recover previous results as limiting cases. Also, following a recent paper by Buchbinder and Tseytlin, we provide relevant four-point functions and consider some of their limits.

Large spin behavior of anomalous dimensions and short–long strings duality

We consider the semi-classical string soliton solution of Gubser, Klebanov and Polyakov which represents highly excited states on the leading Regge trajectory, with large spin in AdS5. A prescription relates this soliton solution with the corresponding field theory operators with many covariant derivatives, whose anomalous scaling dimension grows logarithmically with the spacetime spin. We explicitly derive the coefficients in the large spin expansion of the anomalous dimension in the leading ln nS/Sn and next-to-leading ln nS/Sn + 1 orders. We develop an iteration procedure which, in principle, allows us to derive all terms in the large spin expansion of the anomalous scaling dimension of twist two operators. Our string theory results are consistent with the conjectured ‘reciprocity’ relation, which has been verified to hold in perturbation theory up to five loops in N = 4 SYM. We also derive a duality relation between long and short strings.

Semiclassical short strings in AdS5 × S 5

We present results for the one-loop correction to the energy of a class of string solutions in AdS_5 x S^5 in the short string limit. The computation is based on the observation that, as for rigid spinning string elliptic solutions, the fluctuation operators can be put into the single-gap Lame' form. Our computation reveals a remarkable universality of the form of the energy of short semiclassical strings. This may help to understand better the structure of the strong coupling expansion of the anomalous dimensions of dual gauge theory operators.

Holographic three-point functions of giant gravitons

Working within the AdS/CFT correspondence we calculate the three-point function of two giant gravitons and one pointlike graviton using methods of semiclassical string theory and considering both the case where the giant gravitons wrap an S^3 in S^5 and the case where the giant gravitons wrap an S^3 in AdS_5. We likewise calculate the correlation function in N=4 SYM using two Schur polynomials and a single trace chiral primary. We find that the gauge and string theory results have structural similarities but do not match perfectly, and interpret this in terms of the Schur polynomials' inability to interpolate between dual giant and pointlike gravitons.

Semiclassical string computation of strong-coupling corrections to dimensions of operators in Konishi multiplet

Following our earlier work in arXiv:0906.4294 we show how to use semiclassical string quantization approach to compute the leading corrections to the energy of AdS 5 × S 5 string states on the first excited string level that should correspond to operators in the Konishi multiplet of N = 4 SYM theory. Compared to examples in our previous paper the string solutions we consider here carry an extra component of S 5 angular momentum J. This facilitates their identification with operators in the Konishi multiplet. We show that for such string states with J = 2 the coefficient of the subleading λ − 1 / 4 term in the large string tension expansion of the energy is twice the one found in arXiv:0906.4294. The resulting value matches the one found for the Konishi state in the sl ( 2 ) sector from the Y-system/TBA approach, resolving an apparent disagreement claimed earlier.

Three-point correlation functions from semiclassical circular strings

The strong-coupling limit of three-point correlation functions of local operators can be analyzed beyond the supergravity regime using vertex operators representing spinning string states. When two of the vertex operators correspond to heavy string states having large quantum numbers, while the third operator corresponds to a light state with fixed charges, the correlator can be computed in the large string tension limit by means of a semiclassical approximation. We study the case when the heavy string states are circular string solutions with one AdS5 spin and three different angular momenta along S5, for several choices of the light string state.

Exact computation of one-loop correction to the energy of pulsating strings in AdS5 × S5

In this paper, which is a sequel to Beccaria et al (2010 J. Phys. A: Math. Theor. 43 165402), we compute the one-loop correction to the energy of pulsating string solutions in AdS5 × S5. We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can also be put into the single-gap Lamé form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the ‘short-string’ limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of ‘small’ semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.

Spiky strings and giant holes

We analyse semiclassical strings in AdS in the limit of one large spin. In this limit, classical string dynamics is described by a finite number of collective coordinates corresponding to spikes or cusps of the string. The semiclassical spectrum consists of two branches of excitations corresponding to “large” and “small” spikes respectively. We propose that these states are dual to the excitations known as large and small holes in the spin chain description of \( \mathcal{N} = 4 \) SUSY Yang-Mills. The dynamics of large spikes in classical string theory can be mapped to that of a classical spin chain of fixed length. In turn, small spikes correspond to classical solitons propagating on the background formed by the large spikes. We derive the dispersion relation for these excitations directly in the finite gap formalism.

On the spectral problem of $ \mathcal{N} = 4 $ SYM with orthogonal or symplectic gauge group

We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). At the planar level, the difference to the case of gauge group SU(N) is only due to certain states being projected out, however at the non-planar level novel effects appear: While 1/N-corrections in the SU(N) case are always associated with splitting and joining of spin chains, this is not so for SO(N) and Sp(N). Here the leading 1/N-corrections, which are due to non-orientable Feynman diagrams in the field theory, originate from a term in the dilatation operator which acts inside a single spin chain. This makes it possible to test for integrability of the leading 1/N-corrections by standard (Bethe ansatz) means and we carry out various such tests. For orthogonal and symplectic gauge group the dual string theory lives on the orientifold AdS5xRP5. We discuss various issues related to semi-classical strings on this background.

On the non-BPS string solutions in Sasaki-Einstein gauge/gravity duality

We present an extensive analysis on several string solutions in AdS 5 × Y p,q and find some interesting properties of their energy-spin relations. Their energy depends always on the parameter a(p, q) which characterizes these manifolds. The range of this parameter for the string solutions is constrained by the Sasaki-Einstein constraints that the solutions should satisfy. Hence some string solutions we find are not valid for the whole class of Y p,q manifolds. For some of our solutions, when the maximum allowed value of a(p, q) corresponds to the string approaching the poles of the squashed sphere in Y p,q , their energy at this limit approaches the BPS one. Thus certain non-BPS string solutions in the whole class of Sasaki-Einstein manifolds, can become BPS in particular manifolds. For the solutions with this property we point out that this behavior is independent of the string motion in the other directions on the manifold. We expect that in the field theory the corresponding generic operators to these semi-classical strings, become BPS at certain quivers.

QUANTUM STRINGS IN AdS5 × S5 AND GAUGE–STRING DUALITY

We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 × S5 – planar [Formula: see text] super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 × S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for semiclassical string states to extract information about the leading coefficients in this expansion.

Semiclassical rigid strings with two spins inAdS5

Semiclassical spinning string states in AdS_5 are, in general, characterised by the three SO(2,4) conserved charges: the energy E and the two spins S_1 and S_2. We discuss several examples of explicit classical solutions for rigid closed strings of (bended) circular shape with two non-zero spins. In particular, we identify a solution that should represent a state that has minimal energy for large values of the two equal spins. Similarly to the spiky string in AdS_3, in the large spin limit this string develops long "arcs" that stretch towards the boundary of AdS_5. This allows the string to increase the spin while having the energy growing only logarithmically with S=S_1 +S_2. The large spin asymptotics of such solutions is effectively controlled by their near-boundary parts which, as in the spiky string case, happen to be SO(2,4) equivalent to segments of the straight folded spinning string. As a result, the coefficient of the \log S term in the string energy should be given, up to an overall 3/2 coefficient, by the same universal scaling function (cusp anomaly) as in the folded string case, to all orders in the inverse string tension or strong-coupling expansion.

Semiclassical bosonic D-brane boundary states in curved spacetime

Abstract In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g AB and the constant antisymmetric Kalb-Ramond field b AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.

Quantum strings inAdS5×S5: strong-coupling corrections to dimension of Konishi operator

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.

Semi-classical strings in Sasaki-Einstein manifolds

We find point-like and classical string solutions on the AdS_5 x X^5, where X^5 are the 5-dimensional Sasaki-Einstein manifolds Ypq and Lpqr. The number of acceptable solutions is limited drastically in order to satisfy the constraints on the parameters and coordinates of the manifolds. The energy of the solutions depends on the parameters of the Sasaki-Einstein manifolds and on the conserved momenta transcendentally. A discussion on BPS solutions is presented as well.

Semiclassical strings inAdS3×S2

In this paper, we investigate the semiclassical strings in AdS3 × S2, in which the string configuration of AdS3 is classified to three cases depending on the parameters. Each of these has a different anomalous dimension proportional to log S, S1/3 and S, where S is a angular momentum on AdS3. Further we generalize the dispersion relations for various string configuration on AdS3 × S2.

Non-relativistic CFT and semi-classical strings

We study different features of 3D non-relativistic CFT using gravity description. As the corresponding gravity solution can be embedded into the type IIB string theory, we study semi-classical closed/open strings in this background. In particular we consider folded rotating and circular pulsating closed strings where we find the anomalous dimension of the dual operators as a function of their quantum numbers. We also consider moving open strings in this background which can be used to compute the drag force. In particular we find that for slowly moving particles, the energy is lost exponentially and the characteristic time is given in terms of the temperature, while for fast moving particles the energy loss goes as inverse of the time and the characteristic time is independent of the temperature.

Matching gauge theory and string theory in a decoupling limit of AdS/CFT

We identify a regime of the AdS/CFT correspondence in which we can quantitatively match = 4 super Yang-Mills (SYM) for small 't Hooft coupling with weakly coupled type IIB string theory on AdS5 × S5. We approach this regime by taking the same decoupling limit on both sides of the correspondence. On the gauge theory side only the states in the SU(2) sector survive, and in the planar limit the Hamiltonian is given by the XXX1/2 Heisenberg spin chain. On the string theory side we show that the decoupling limit corresponds to a non-relativistic limit. In this limit some of the bosonic modes and all of the fermionic modes of the string become infinitely heavy and decouple. We first take the decoupling limit of the string sigma-model classically. This enables us to identify a semi-classical regime with semi-classical string states even though we are in a regime corresponding to small 't Hooft coupling. We furthermore analyze the quantum corrections that enter in taking the limit. From this we infer that gauge theory and string theory match, both in terms of the action and the spectrum, for the leading part and the first correction away from the semi-classical regime. Finally we consider the implications for the hitherto unexplained matching of the one-loop contribution to the energy of certain gauge theory and string theory states, and we explain how our results give a firm basis for the matching of the Hagedorn temperature in hep-th/0608115.