Shijong Ryang

Correlators of vertex operators for circular strings with winding numbers in AdS5 × S5

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 AdS5 and three large spins and three winding numbers in S5. 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.

Three-spin giant magnons in AdS5 × S5

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.

Giant magnon and spike solutions with two spins in AdS4 × CP3

In the string theory in AdS4 × CP3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of Rt × CP3 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 RP2 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 S2 subspace but has one additional spin dependence.

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

Abstract 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.

Wound and rotating strings in AdS5 × S5

From the Nambu-Goto string action using a non-diagonal gauge we construct a solution describing a wound string in AdS5 × S5 which rotates in the same angular direction as the winding direction in S5. 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 integrable hamiltonian constructed in hep-th/0411089 by using the non-diagonal uniform gauge for the Polyakov string action. We analyze a wound string solution which is rotating in the different angular direction from the winding direction.

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 S5 spins (J1,J2) in the AdS5 ? S5 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 AdS5 spin S and one S5 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 (S1,S2,J).

Algebraic Curves for Long Folded and Circular Winding Strings in AdS 5 ×S 5

A bstractFor 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 AdS3 has the same algebraic curve as the null cusp Wilson loop. The algebraic curve for the circular winding string in AdS3 × S1 is evaluated. The Virasoro constraint is discussed to characterize the branch points of each curve.

The Picard-Fuchs equations, monodromies and instantons in the N = 2 SUSY gauge theories

Abstract We construct the Picard-Fuchs equations of the N = 2 supersymmetric SU(2) gauge theories with Nf = 0, 1, 3 matter multiplets. For the Nf = 0 theory from the solutions of the Picard-Fuchs equation the monodromy matrices on the quantum moduli space are determined. We analyze the Seiberg-Witten solutions to compute monodromies exactly and present the instanton expansion of the periods for the Nf = 0, 3 theories.

Three-Point Correlator of Heavy Vertex Operators for Circular Winding Strings in AdS 5 × S 5

Abstract We consider an extremal three-point correlator of three heavy vertex operators for the circular winding string state with one large spin and one winding number in AdS 5 and one large spin and one winding number in S 5 . 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.

Rotating and orbiting strings in the near-horizon brane backgrounds

Using the Schwarzschild-type coordinates in stead of the global ones we reconstruct the classical rotating closed string solutions in the AdS5 × S5 backgrounds. They are explicitly described by the Jacobi elliptic and trigonometrical functions of worldsheet coordinates. We study the orbiting closed string configurations in the near-horizon geometries of Dp, NS1 and NS5 branes, and derive the energy and spin of them, whose relation takes a simple form for short strings. Specially in the D5 and NS5 backgrounds we have a linear relation that the energy of the point-like string is proportional to the spin, which is associated with the spectrum of strings in the pp-wave geometries obtained by taking a special Penrose limit on the D5 and NS5 backgrounds.