Putting string/string duality to the test

TL;DR

This paper tests the string/string duality in six dimensions by comparing anomaly polynomials of dual strings, providing evidence for the duality conjecture and insights into vacuum degeneracy.

Contribution

It offers a classical calculation of the dual string's anomaly polynomial, confirming the duality with the fundamental string and supporting previous assumptions.

Findings

Agreement between classical dual string calculation and quantum fundamental string results

Validation of the string/string duality conjecture in six dimensions

Implications for understanding vacuum degeneracy in string theory

Abstract

After simultaneous compactification of spacetime and worldvolume on $K3$, the $D=10$ heterotic fivebrane with gauge group $SO(32)$ behaves like a $D=6$ heterotic string with gauge group $SO(28) \times SU(2)$, but with Kac--Moody levels different from those of the fundamental string. Thus the string/fivebrane duality conjecture in $D=10$ gets replaced by a string/string duality conjecture in $D=6$. Since $D=6$ strings are better understood than $D=10$ fivebranes, this provides a more reliable laboratory in which to test the conjecture. According to string/string duality, the Green--Schwarz factorization of the $D=6$ spacetime anomaly polynomial $I_{8}$ into $X_4\, \tilde{X}_4$ means that just as $X_4$ is the $\sigma$-model anomaly polynomial of the fundamental string worldsheet so $\tilde{X}_4$ should be the corresponding polynomial of the dual string worldsheet. To test this idea we perform a classical dual string calculation of $\tilde{X}_4$ and find agreement with the quantum fundamental string result. This also provides an {\it a posteriori} justification for assumptions made in a previous paper on string/fivebrane duality. Finally we speculate on the relevance of string/string duality to the vacuum degeneracy problem.