Membrane Duality Revisited

Abstract

Just as string T-duality originates from transforming field equations into Bianchi identities on the string worldsheet, so it has been suggested that M-theory U-dualities originate from transforming field equations into Bianchi identities on the membrane worldvolume. However, this encounters a problem unless the target space has dimension $D=p+1$. We identify the problem to be the nonintegrability of the U-duality transformation assigned to the pull-back map. Just as a double geometry renders manifest the $O(D,D)$ string T-duality, here we show in the case of the M2-brane in $D=3$ that a generalised geometry renders manifest the $SL(3)\times SL(2)$ U-duality. In the case of M2-brane in $D=4$, with and without extra target space coordinates, we show that only the $\mathrm{GL}(4,R)⋉R^4$ subgroup of the expected $SL(5,R)$ U-duality symmetry is realised.

26 pages

References in corpus (11)

• Double Field Theory
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• Exceptional Field Theory III: E${}_{8(8)}$
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• E${}_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB
• Ramond-Ramond gauge fields in superspace with manifest T-duality
• Critical Super F-theories
• M-branes on U-folds
• Non-commutativity from the double sigma model
• Equivalence of open/closed strings

Cited by in corpus (16)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Non-Riemannian geometry of M-theory
• Non-Abelian U-duality for membrane
• The Exceptional Sigma Model
• Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry
• World-volume Effective Action of Exotic Five-brane in M-theory
• Exceptional M-brane sigma models and $\eta$-symbols
• Doubled strings, negative strings and null waves
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Type II strings are Exceptional
• Particle actions and brane tensions from double and exceptional geometry
• Currents, charges and algebras in exceptional generalised geometry
• Extended Drinfel'd algebras and non-Abelian duality
• Classical worldvolumes as generalised geodesics
• U-duality transformation of membrane on $T^n$ revisited
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations