Exceptional M-brane sigma models and $\eta$-symbols

TL;DR

This paper constructs U-duality-covariant M-brane actions using eta-symbols, generalizing self-duality relations and reproducing known brane actions, including M5-branes and (p,q)-strings.

Contribution

It introduces eta-forms and develops a unified formalism for M-branes, extending self-duality and incorporating type IIB branes within a covariant framework.

Findings

Unified M-brane actions with eta-symbols and eta-forms.

Generalized self-duality relations for M-branes.

Reproduction of known brane actions, including M5 and (p,q)-strings.

Abstract

We develop the M-brane actions proposed in arXiv:1607.04265 by using $\eta$-symbols determined in arXiv:1708.06342. Introducing $\eta$-forms that are defined with the $\eta$-symbols, we present U-duality-covariant M-brane actions which describe the known brane worldvolume theories for M$p$-branes with $p=0,2,5$. We show that the self-duality relation known in the double sigma model is naturally generalized to M-branes. In particular, for an M5-brane, the self-duality relation is nontrivially realized, where the Hodge star operator is defined with the familiar M5-brane metric while the $\eta$-form contains the self-dual 3-form field strength. The action for a Kaluza-Klein monopole is also partially reproduced. Moreover, we explain how to treat type IIB branes in our general formalism. As a demonstration, we reproduce the known action for a $(p,q)$-string.