Penrose Limit and String Theories on Various Brane Backgrounds

TL;DR

This paper explores the Penrose limit of various brane solutions, deriving string theories with both constant and time-dependent masses, and solving string equations of motion in complex backgrounds.

Contribution

It provides a comprehensive analysis of Penrose limits on diverse brane backgrounds, including explicit solutions involving spheroidal wave functions.

Findings

String theories with constant mass are obtained at critical radii.

Time-dependent mass string theories are derived from brane backgrounds.

Explicit solutions for string equations of motion involve spheroidal wave functions.

Abstract

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.