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We develop the M-brane actions proposed in arXiv:1607.04265 by using$\eta$-symbols determined in arXiv:1708.06342. Introducing $\eta$-forms thatare defined with the $\eta$-symbols, we present U-duality-covariant M-braneactions which describe the known brane worldvolume theories for M$p$-braneswith $p=0,2,5$. We show that the self-duality relation known in the doublesigma model is naturally generalized to M-branes. In particular, for anM5-brane, the self-duality relation is nontrivially realized, where the Hodgestar operator is defined with the familiar M5-brane metric while the$\eta$-form contains the self-dual 3-form field strength. The action for aKaluza-Klein monopole is also partially reproduced. Moreover, we explain how totreat type IIB branes in our general formalism. As a demonstration, wereproduce the known action for a $(p,q)$-string.

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