T-Duality Transformation and Universal Structure of Non-Critical String Field Theory

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. The duality symmetry is however violated when the higher-genus effects are taken into account, owing to the existence of global Z_2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by the last two authors are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators.Comment: RevTex, 46 pages, 5 eps figure

Boundary fields and renormalization group flow in the two-matrix model

We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary field. The results of these calculations can be interpreted in terms of renormalization group flow induced by the boundary operator. In the continuum limit this RG flow corresponds to the flow from non-conformal to conformal boundary conditions which has recently been studied in flat space theories.Comment: 31 pages, Late

Quantifying Progress in Research Topics Across Nations

A scientist’s choice of research topic affects the impact of their work and future career. While the disparity between nations in scientific information, funding, and facilities has decreased, scientists on the cutting edge of their fields are not evenly distributed across nations. Here, we quantify relative progress in research topics of a nation from the time-series comparison of reference lists from papers, using 71 million published papers from Scopus. We discover a steady leading-following relationship in research topics between Western nations or Asian city-states and others. Furthermore, we find that a nation’s share of information-rich scientists in co-authorship networks correlates highly with that nation’s progress in research topics. These results indicate that scientists’ relationships continue to dominate scientific evolution in the age of open access to information and explain the failure or success of nations’ investments in science