Putting String/Fivebrane Duality to the Test

TL;DR

This paper tests the string/fivebrane duality hypothesis by calculating the anomaly polynomial for the fivebrane and confirming it matches the known string result, supporting the duality concept.

Contribution

It provides a direct fivebrane calculation of the anomaly polynomial $X_8$, confirming its agreement with the string one-loop result, thus supporting the duality.

Findings

$X_8$ matches the string one-loop anomaly polynomial

Supports the string/fivebrane duality hypothesis

Provides a concrete fivebrane calculation of anomaly polynomial

Abstract

According to string/fivebrane duality, the Green-Schwarz factorization of the $D=10$ spacetime anomaly polynomial $I_{12}$ into $X_4\, X_8$ means that just as $X_4$ is the anomaly polynomial of the $d=2$ string worldsheet so $X_8$ should be the anomaly polynomial of the $d=6$ fivebrane worldvolume. To test this idea we perform a fivebrane calculation of $X_8$ and find perfect agreement with the string one--loop result.