Heterotic and type I strings from twisted supermembranes

TL;DR

This paper demonstrates that twisted supermembranes in M-theory naturally lead to the low-energy limit of the $E_8\times E_8$ heterotic string and explores related dualities and anomaly cancellation conditions.

Contribution

It shows that supermembranes on specific manifolds produce heterotic string theories and aligns anomaly cancellation conditions with those of Ho\v{r}ava-Witten theory.

Findings

Effective action matches $E_8\times E_8$ heterotic string in small $S^1/Z_2$ limit

Dualities consistent with 11D supergravity expectations

Anomaly cancellation conditions align with Ho\v{r}ava-Witten requirements

Abstract

As shown by Ho\v{r}ava and Witten, there are gravitational anomalies at the boundaries of $M^{10}\times S^1/Z_2$ of 11 dimensional supergravity. They showed that only 10 dimensional vector multiplets belonging to $E_8$ gauge group can be consistently coupled to this theory. Thus, the dimensional reduction of this theory should be the low energy limit of the $E_8\times E_8$ heterotic string. Here we assume that M-theory is a theory of supermembranes which includes twisted supermembranes. We show that for a target space $M^{10}\times S^1/Z_2$, in the limit in which $S^1/Z_2$ is small, the effective action is the $E_8\times E_8$ heterotic string. We also consider supermembranes on $M^{9}\times S^1\times S^1/Z_2$ and find the dualities expected from 11 dimensional supergravity on this manifold. We show that the requirements for worldsheet anomaly cancellations at the boundaries of the worldvolume action are the same requirements imposed on the Ho\v{r}ava-Witten action.