Heterotic/Heterotic Duality in D=6,4

TL;DR

This paper explores heterotic/heterotic duality in six and four dimensions, proposing an alternative to symmetric embeddings that accounts for spontaneous symmetry breaking and analyzing the resulting gauge theories and dual models.

Contribution

It introduces an asymmetric embedding approach to heterotic duality, addressing issues with negative kinetic terms and expanding the understanding of dual models in various dimensions.

Findings

Asymmetric embeddings lead to different beta-function values (${\beta}_\alpha=24$).

Dual models exhibit consistent gauge kinetic functions in large $T,S$ limits.

Freely acting twists produce dual $N=1$, $D=4$ models.

Abstract

We consider $E_8\times E_8$ heterotic compactifications on $K3$ and $K3\times T^2$. The idea of heterotic/heterotic duality in $D=6$ has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both $E_8$'s. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to $D=4$, we find that the duals in the DMW case correspond to $N=2$ models in which the $\beta$-function of the different group factors verify ${\beta }_\alpha=12$, whereas the asymmetric solutions that we propose have ${\beta }_\alpha=24$. We check the consistency of these dualities by studying the different large $T,S$ limits of the gauge kinetic function. Dual $N=1$, $D=4$ models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples.