Factorization and Unitarity in Superstring Theory

The overall coefficient of the two-loop 4-particle amplitude in superstring theory is determined by making use of the factorization and unitarity. To accomplish this we computed in detail all the relevant tree and one-loop amplitudes involved and determined their overall coefficients in a consistent way.Comment: LaTex file, 19 pages, 4 figures; v2, minor corrections and figures corrected; v3, minor corrections with the English, to be published in JHE

Electromagnetic response of high-Tc superconductors -- the slave-boson and doped-carrier theories

We evaluate the doping dependence of the quasiparticle current and low temperature superfluid density in two slave-particle theories of the tt't''J model -- the slave-boson theory and doped-carrier theory. In the slave-boson theory, the nodal quasiparticle current renormalization factor $\alpha$ vanishes proportionally to the zero temperature superfluid density $\rho_S(0)$; however, we find that away from the $\rho_S(0) \to 0$ limit $\alpha$ displays a much weaker doping dependence than $\rho_S(0)$. A similar conclusion applies to the doped-carrier theory, which differentiates the nodal and antinodal regions of momentum space. Due to its momentum space anisotropy, the doped-carrier theory enhances the value of $\alpha$ in the hole doped regime, bringing it to quantitative agreement with experiments, and reproduces the asymmetry between hole and electron doped cuprate superconductors. Finally, we use the doped-carrier theory to predict a specific experimental signature of local staggered spin correlations in doped Mott insulator superconductors which, we propose, should be observed in STM measurements of underdoped high-Tc compounds. This experimental signature distinguishes the doped-carrier theory from other candidate mean-field theories of high-Tc superconductors, like the slave-boson theory and the conventional BCS theory.Comment: 12 pages, RevTeX4, homepage http://dao.mit.edu/~we

Exact Algorithms for Maximum Independent Set

We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of $1.1893^nn^{O(1)}$ and $1.1970^nn^{O(1)}$, respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analyses on the structure of bounded-degree graphs

Non-Universality of Transverse Momentum Dependent Parton Distributions at Small-x

We study the universality issue of the transverse momentum dependent parton distributions at small-x, by comparing the initial/final state interaction effects in dijet-correlation in pA collisions with those in deep inelastic lepton nucleus scattering. We demonstrate the non-universality by performing an explicit calculation in a particular model where the multiple gauge boson exchange contributions are summed up to all orders. We comment on the implications of our results on the theoretical interpretation of di-hadron correlation in dA collisions in terms of the saturation phenomena in deep inelastic lepton nucleus scattering.Comment: 11 pages, 3 figure

Driving light pulses with light in two-level media

A two-level medium, described by the Maxwell-Bloch (MB) system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the MB system with variable boundary driving is obtained as a discrete nonlinear Schroedinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse

Factorization of the Two Loop Four-Particle Amplitude in Superstring Theory Revisited

We study in detail the factorization of the newly obtained two-loop four-particle amplitude in superstring theory. In particular some missing factors from the scalar correlators are obtained correctly, in comparing with a previous study of the factorization in two-loop superstring theory. Some details for the calculation of the factorization of the kinematic factor are also presented.Comment: 11 pages, 1 figure; v2, minor corrections and references update