Penrose Limit and Enhancon Geometry

TL;DR

This paper investigates superstring theories on the Penrose limit of enhancon geometries, analyzing null geodesics, mass-squared conditions, and the dual gauge theories, revealing p=0 as a special case with positive mass-squared.

Contribution

It identifies conditions for positive mass-squared in superstring theories on enhancon geometries and characterizes the existence of null geodesics for different p-brane cases.

Findings

Null geodesics with fixed radius exist only for p=0.

Superstring theories have positive mass-squared only in the p=0 case.

The spectrum depends on the K3-volume and the decoupling limit.

Abstract

We study superstring theories on the Penrose limit of the enhancon geometry realized by the D(p+4)-branes wrapped on a K3 surface. We first examine the null geodesics with fixed radius in general brane backgrounds, which give solvable superstring theories with constant masses. In most cases, the superstring theories contain negative mass-squared. We clarify a condition that the world-sheet free fields have positive mass-squared. We then apply this condition to the enhancon geometry and find that the null geodesics with fixed radius exist only for p=0 case. They define the superstring theories with positive mass-squared. For p>0 case, we show that there is no null geodesic with fixed radius. We also discuss the decoupling limit which gives the dual geometry of super Yang-Mills theory with 8 supercharges. We discuss the K3-volume dependence of the superstring spectrum.