Year: 2012
Type: article
Abstract: The evaluation of the determinant of the Laplacian defined on two dimensional regions of various shapes is an essential ingredient in calculating the scattering amplitudes of strings. In lightcone parameterization the regions are rectangular in shape with several slits of different length and location cut parallel to the $\ensuremath{\tau}$ axis of the rectangle. This paper offers a compendium of applications of the methods of Kac and McKean and Singer to the calculation of such worldsheet determinants. Particular attention is paid to the effect of corners on the determinants. The effect of corners joining edges with like boundary conditions is implicit in Kac's results. We discuss the generalization to a corner joining a Dirichlet edge to a Neumann edge, and apply it to a scattering amplitude involving D-branes.
Author: Charles B. Thorn
Institution: University of Florida
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W2013300854