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

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.

55 pages; v2: references added, minor improvements; v3: clarifications added, to appear in PTEP; v4: typos corrected

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Cited by in corpus (11)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Non-Riemannian geometry of M-theory
• Non-relativistic duality and $T\bar{T}$ deformations
• Non-Abelian U-duality for membrane
• Born sigma model for branes in exceptional geometry
• Currents, charges and algebras in exceptional generalised geometry
• Open exceptional strings and D-branes
• Poisson-Lie T-plurality for dressing cosets
• Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations