arXiv subjects

Shijong Ryang

Publications and source records attributed to Shijong Ryang.

At least 19 recordsLinked to original sources

arXiv2014

Conformal Transformations and Strings for an Accelerating Quark-Antiquark Pair in AdS3

From a simple moving open string solution dual to a moving heavy quark with constant velocity in the Poincare AdS_3 spacetime, we construct an accerlerating open string solution dual to a heavy quark-antiquark pair accelerated in opposite directions by performing the three mappings such as the SL(2,R)_L x SL(2,R)_R isometry transformation, the special conformal transformation and the conformal SO(2,2) transformation. Using the string sigma model action we construct two open string solutions staying in two different regions whose dividing line is associated with the event horizon appeared on the string worldsheet and obtain the accelerating open string solution by gluing two such solutions.

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arXiv2013

BPS Wilson Loop T-dual to Spinning String in AdS5xS5

We use the string sigma model action in AdS_5 \times S^5 to reconstruct the open string solution ending on the Wilson loop in S^3\times R parametrized by a geometric angle in S^3 and an angle in flavor space. Under the interchange of the world sheet space and time coordinates and the T-duality transformation with the radial inversion, the static open string configuration associated with the BPS Wilson loop with two equal angle parameters becomes a long open spinning string configuration which is produced by taking the equal limit of two frequencies for the folded spinning closed string with two spins in AdS_5 \times S^5.

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arXiv2012

Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5

For the homogeneous configuration given by the long string limit of the folded string with a spin in AdS3 and a spin and a winding number in S1, we solve the auxiliary linear problem in the finite-gap method and construct the Lax operator to obtain an algebraic curve. We show that the long spiky string in AdS_3 has the same algebraic curve as the null cusp Wilson loop. The algebraic curve for the circular winding string in AdS3xS1 is evaluated. The Virasoro constraint is discussed to characterize the branch points of each curve.

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arXiv2012

Three-Point Correlator of Heavy Vertex Operators for Circular Winding Strings in AdS5xS5

We consider an exremal three-point correlator of three heavy vertex operators for the circular winding string state with one large spin and one windining number in AdS5 and one large spin and one winding number in S5. We use a Schwarz-Christoffel transformation to compute semiclassically the extremal three-point correlator on a stationary string trajectory which is mapped to the complex plane with three punctures. It becomes a 4d conformal invariant three-point correlator on the boundary. We discuss the marginality condition of vertex operator.

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arXiv2011

Extremal Correlator of Three Vertex Operators for Circular Winding Strings in AdS5xS5

We study a three-point correlator of the three heavy vertex operators representing the circular winding string states which are point-like in AdS_5 and rotating with two spins and two winding numbers in S^5. We restrict ourselves to the case that two of the three vertex operators are located at the same point. We evaluate semiclassically the specific three-point correlator on a stationary splitting string trajectory which is mapped to the complex plane with three punctures. It becomes an extremal and 4d conformal invariant three-point correlator on the boundary. The marginality condition of the vertex operator is discussed.

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arXiv2010

Correlators of Vertex Operators for Circular Strings with Winding Numbers in AdS5xS5

We compute semiclassically the two-point correlator of the marginal vertex operators describing the rigid circular spinning string state with one large spin and one windining number in AdS_5 and three large spins and three winding numbers in S^5. The marginality condition and the conformal invariant expression for the two-point correlator obtained by using an appropriate vertex operator are shown to be associated with the diagonal and off-diagonal Virasoro constraints respectively. We evaluate semiclassically the three-point correlator of two heavy circular string vertex operators and one zero-momentum dilaton vertex operator and discuss its relation with the derivative of the dimension of the heavy circular string state with respect to the string tension.

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arXiv2010

Spiky Strings with Two Spins in AdS5

Using the reduction of the string sigma model to the 1-d Neumann integrable model we reconstruct the closed string solution with two equal spins in AdS_5 which is specified by the number of round arcs and one winding number. From the string sigma model itself as well as its reducion to the Neumann-Rosochatius system we construct a spiky string solution with two unequal spins in AdS_5 whose ratio is fixed and derive its energy-spin relation. The string configuration is characterized by the number of spikes and two equal winding numbers associated with the two rotating angular directions.

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arXiv2009

Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}

For the asymptotic string solution in AdS_3 which is represented by the AdS_3 Poincare coordinates and yields the planar multi-gluon scattering amplitude at strong coupling in arXiv:0904.0663, we express it by the AdS_4 Poincare coordinates and demonstrate that the hexagonal and octagonal Wilson loops surrounding the string surfaces take closed contours consisting of null vectors in R^{1,2} owing to the relations of Stokes matrices. For the tetragonal Wilson loop we construct a string solution characterized by two parameters by solving the auxiliary linear problems and demanding a reality condition, and analyze the asymptotic behavior of the solution in R^{1,2}. The freedoms of two parameters are related with some conformal SO(2,4) transformations.

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arXiv2009

Janus Field Theories from Non-Linear BF Theories for Multiple M2-Branes

We integrate the nonpropagating B_μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M^{IJK} in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M^{IJK} as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A_μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B_μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

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arXiv2008

Giant Magnon and Spike Solutions with Two Spins in AdS4xCP3

In the string theory in AdS_4 \times CP^3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of R_t \times CP^3 and derive the dispersion relations for them. For the single giant magnon solution in one subspace we show that its dispersion relation is associated with that of the big one-spin giant magnon solution in the RP^2 subspace. For the single giant magnon solution in the other complementary subspace its dispersion relation is similar to that of the one-spin giant magnon solution living in the S^2 subspace but has one additional spin dependence.

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arXiv2008

Conformal SO(2,4) Transformations for the Helical AdS String Solution

By applying the conformal SO(2,4) transformations to the folded rotating string configuration with two spins given by a certain limit from the helical string solution in AdS_3 x S^1, we construct new string solutions whose energy-spin relations are characterized by the boost parameter. When two SO(2,4) transformations are performed with two boost parameters suitably chosen, the straight folded rotating string solution with one spin in AdS_3 is transformed in the long string limit into the long spiky string solution whose expression is given from the helical string solution in AdS_3 by making a limit that the modulus parameter becomes unity.

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arXiv2007

Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface

By applying the conformal SO(2,4) transformations to the elementary one-cusp Wilson loop surface we construct various two-cusp and four-cusp Wilson loop surface configurations in AdS_5 and demonstrate that they solve the string equations of the Nambu-Goto string action. The conformal boosts of the basic four-cusp Wilson loop surface with a square-form projection generate various four-cusp Wilson loop surfaces with projections of the rescaled square, the rhombus and the trapezium, on which surfaces the classical Euclidean Nambu-Goto string actions in the IR dimensional regularization are evaluated.

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arXiv2007

Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors

We construct the integral equations by taking the thermodynamic limit of both the all-loop gauge Bethe ansatz equation and the string Bethe ansatz equation for the highest states in the su(1|1) and su(2) sectors of the N=4 super Yang-Mills theory. Using the Fourier transformation we solve the integral equations iteratively to obtain the anomalous dimensions of the highest states in the weak coupling expansion. In the su(1|1) sector we analytically study the strong coupling limit of the anomalous dimension for the all-loop gauge Bethe ansatz equation by means of the Laplace transformation.

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arXiv2006

Three-Spin Giant Magnons in AdS_5xS^5

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.

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arXiv2006

The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5

For the κ-symmetry gauge fixed superstring action in AdS_5 x S^5 we consider the fermionic fluctuations over a circular bosonic string background with two angular momenta and two winding numbers in S^5. The SU(2)-type redefinitions of fermionic fields and the first-string limit generate a truncated fermionic action for the SU(1|2) sector. It is expressed in a two-dimensional Lorentz-invariant form of a massive Dirac fermion and the plane-wave spectrum for the fermionic excitations is derived. The fermionic spectrum for the SU(2|2) sector is also analyzed.

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arXiv2005

Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background

We study a string motion in the Lunin-Maldacena background, that is, the β-deformed AdS_5 \times \tilde{S}^5 background dual to a β-deformation of \mathcal{N} = 4 super Yang-Mills theory. For real βwe construct a rotating and wound string solution which has two unequal spins in \tilde{S}^5. The string energy is expressed in terms of the spins, the winding numbers and the deformation parameter. In the expansion of λ/J^2 with the total spin J and the string tension \sqrtλ we present ``one-loop" and ``two-loop" energy corrections. The ``one-loop" one agrees with the one-loop anomalous dimension of the corresponding gauge-theory scalar operators obtained in hep-th/0503192 from the β-deformed Bethe equation as well as the anisotropic Landau-Lifshitz equation.

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arXiv2005

Wound and Rotating Strings in AdS_5 x S^5

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.

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arXiv2004

Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models

From the SU(2) spin chain sigma model at the one-loop and two-loop orders we recover the classical circular string solution with two S^5 spins (J_1, J_2) in the AdS_5 x S^5 string theory. In the SL(2) sector of the one-loop spin chain sigma model we explicitly construct a solution which corresponds to the folded string solution with one AdS_5 spin S and one S^5 spin J. In the one-loop general sigma model we demonstrate that there exists a solution which reproduces the energy of the circular constant-radii string solution with three spins (S_1, S_2, J).

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