Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence

We consider defect composite operators in a defect superconformal field theory obtained by inserting an AdS_4 x S^2-brane in the AdS_5 x S^5 background. The one-loop dilatation operator for the scalar sector is represented by an integrable open spin chain. We give a description to construct coherent states for the open spin chain. Then, by evaluating the expectation value of the Hamiltonian with the coherent states in a long operator limit, a Landau-Lifshitz type of sigma model action is obtained. This action is also derived from the string action and hence we find a complete agreement in both SYM and string sides. We see that an SO(3)_H pulsating string solution is included in the action and its energy completely agrees with the result calculated in a different method. In addition, we argue that our procedure would be applicable to other AdS-brane cases.Comment: 22 pages, 1 figure, LaTeX, minor corrections and references added. v3) some new results added. shortened and accepted version in PR

Semiclassical Strings in Electric and Magnetic Fields Deformed AdS5×S5AdS_5 \times S^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 $AdS_5 \times S^5$. We adopt an ansatz to find the classical string solution which is rotating in the deformed $S^5$ 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 possible 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.Comment: Latex 18 pages, correct sec. 3.

Spin chain from membrane and the Neumann-Rosochatius integrable system

We find membrane configurations in AdS_4 x S^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_5 x S^5. We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases.Comment: LaTeX, 16 pages, no figures; v2: 17 pages, title changed, explanations and references added; v3: more explanations added; v4: typos fixed, to appear in Phys. Rev.

Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality

We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N=4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.Comment: 18 pages, one eps figure, v3: typos corrected, clarifying footnotes added, treatment of complex roots revise

New Integrable Structures in Large-N QCD

We study the anomalous dimensions of single trace operators composed of field strengths $F_{\mu\nu}$ in large-N QCD. The matrix of anomalous dimensions is the Hamiltonian of a compact spin chain with two spin one representations at each vertex corresponding to the selfdual and anti-selfdual components of $F_{\mu\nu}$. Due to the special form of the interaction it is possible to study separately renormalization of purely selfdual components. In this sector the Hamiltonian is integrable and can be exactly solved by Bethe ansatz. Its continuum limit is described by the level two SU(2) WZW model.Comment: 12 pages; V2: ref. added, V3: refs. added, explicit expression for the spin ladder and other text improvement

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.Comment: 21 pages, 8 figure

Exactly stable non-BPS spinors in heterotic string theory on tori

Considering SO(32) heterotic string theory compactified on a torus of dimension 4 and less, stability of non-supersymmetric states is studied. A non-supersymmetric state with robust stability is constructed, and its exact stability is proven in a large region of moduli space against all the possible decay mechanisms allowed by charge conservation. Using various T-duality transform matrices, we translate various selection rules about conserved charges into simpler problems resembling partition and parity of integers. For heterotic string on T^4, we give a complete list of BPS atoms with elementary excitations, and we study BPS and non-BPS molecules with various binding energies. Using string-string duality, the results are interpreted in terms of Dirichlet-branes in type IIA string theory compactified on an orbifold limit of a K3 surface.Comment: 47 pages, 14 figures, LaTe

Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections

We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We compute the generalized scaling function at two-loop order f_2(ell) both for small and large values of ell matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ell expansion, we derive an exact integral form for the ell-dependent coefficient of the Catalan's constant term in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman diagrams we obtain an exact expression for the leading (ln ell) part of f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2) expansion. At large ell the string energy has a BMN-like expansion and the first few leading coefficients are expected to be the same at weak and at strong coupling. We provide a new example of this non-renormalization for the term which is generated at two loops in string theory and at one-loop in gauge theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for the term of maximal transcendentality in f_2(ell) expanded at large ell. In the second part of the paper we initiate the study of 2-loop finite size corrections to the string energy by formally compactifying the spatial world-sheet direction in the string action expanded near long fast-spinning string. We observe that the leading finite-size corrections are of "Casimir" type coming from terms containing at least one massless propagator. We consider in detail the one-loop order (reproducing the leading Landau-Lifshitz model prediction) and then focus on the two-loop contributions to the (1/ln S) term (for J=0). We find that in a certain regularization scheme used to discard power divergences the two-loop coefficient of the (1/ln S) term appears to vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde

Semiclassical Strings on AdS_5 x S^5/Z_M and Operators in Orbifold Field Theories

We show agreements, at one-loop level of field theory, between energies of semiclassical string states on AdS_5 x S^5/Z_M and anomalous dimensions of operators in N=0,1,2 orbifold field theories originating from N=4 SYM. On field theory side, one-loop anomalous dimension matrices can be regarded as Hamiltonians of spin chains with twisted boundary conditions. These are solvable by Bethe ansatz. On string side, twisted sectors emerge and we obtain some string configurations in twisted sectors. In SU(2) subsectors, we compare anomalous dimensions with string energies and see agreements. We also see agreements between sigma models of both sides in SU(2) and SU(3) subsectors.Comment: LaTeX, 23 pages, 4 figures; v2 minor corrections, added references; v3 typos corrected, published versio

Semiclassical Analysis of M2-brane in AdS_4 x S^7 / Z_k

We start from the classical action describing a single M2-brane on AdS_4 x S^7/ Z_k and consider semiclassical fluctuaitions around a static, 1/2 BPS configuration whose shape is AdS_2 x S^1. The internal manifold S^7/ Z_k is described as a U(1) fibration over CP^3 and the static configuration is wrapped on the U(1) fiber. Then the configuration is reduced to an AdS_2 world-sheet of type IIA string on AdS_4 x CP^3 through the Kaluza-Klein reduction on the S^1. It is shown that the fluctuations form an infinite set of N=1 supermultiplets on AdS_2, for k=1,2. The set is invariant under SO(8) which may be consistent with N=8 supersymmetry on AdS_2. We discuss the behavior of the fluctuations around the boundary of AdS_2 and its relation to deformations of Wilson loop operator.Comment: 27 pages, v2: references added, v3: major revision including the clarification of k=2 case, references added, version to appear in JHE