Three-loop planar master integrals for heavy-to-light form factors

We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be determined, and the solution of differential equations is greatly simplified. The results for seventy-one master integrals at general kinematics are all expressed in terms of harmonic polylogarithms.Comment: 18 pages, 2 figure

Classical Aspects of Higher Spin Topologically Massive Gravity

We study the classical solutions of three dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first order formulation. The action of higher spin TMG has been proposed in arXiv:1110.5113 to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS$_3$ gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair, and find that the nonvanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors.Comment: 25 pages; minor corrections, references added, published versio

The Fate of Massive Closed Strings

We calculate the semi-inclusive decay rate of an average string state with toroidal compactification in the the superstring theory. We also apply this calculation to a brane-inflation model in a warped geometry and find that the decay rate is greatly suppressed if the final strings are both massive and enhanced for massless radiation.Comment: 4 pages, to appear in the proceeding of PASCOS 2005, Gyeongju, Korea, May 30-June 4, 200

Quasinormal Modes and Hidden Conformal Symmetry of Warped dS3_3 Black Hole

In this paper, we analytically calculate the quasinormal modes of scalar, vector, tensor, and spinor perturbations of the warped dS$_3$ black hole. There are two horizons for the warped dS$_3$ black hole, namely, the black hole horizon $r_b$ and the cosmological horizon $r_c$. In the calculation, we impose the ingoing boundary condition at the black hole horizon and the outgoing boundary condition at the cosmological horizon. We also investigate the hidden conformal symmetry of the warped dS$_3$ black hole in the region between the black hole horizon and the cosmological horizon $r_b<r<r_c$. We use the hidden conformal symmetry to construct the quasinormal modes in an algebraic way and find that the results agree with the analytically ones. It turns out that the frequencies of the quasinormal modes could be identified with the poles in the thermal boundary-boundary correlators.Comment: 26 pages, references added, published versio

Exact solution and magnetic properties of an anisotropic spin ladder

We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung interaction. Exact rung states and rung energies are obtained for the anisotropic rung coupling in the presence of a magnetic field. Magnetic properties are analyzed at both zero and finite temperatures via the thermodynamic Bethe ansatz and the high-temperature expansion. According to different couplings in the anisotropic rung interaction, there are two cases in which a gap opens, with the ground state involving one or two components in the absence of a magnetic field. We obtain the analytic expressions of all critical fields for the field-induced quantum phase transitions (QPT). Anisotropic rung interaction leads to such effects as separated magnetizations and susceptibilities in different directions, lowered inflection points and remnant weak variation of the magnetization after the last QPT.Comment: 9 pages, 8 figures; a typo in C_2(below eq.7) correcte