A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry

Abstract

We consider a non-relativistic limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a covariant `membrane Newton-Cartan' (MNC) geometry. The local tangent space is split into three `longitudinal' and eight `transverse' directions, related only by Galilean rather than Lorentzian symmetries. This generalises the ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The finite action then gives a set of equations that is invariant under longitudinal and transverse rotations, Galilean boosts and local dilatations. We supplement these equations with an extra Poisson equation, coming from the subleading action. Reduction along a longitudinal direction gives the known SNC theory with the addition of RR gauge fields, while reducing along a transverse direction yields a new non-relativistic theory associated to D2 branes. We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

52 pages + appendices, v2: matches published version, one word added to title, v3: corrected eqns (4.8), (4.9), (4.10)

References in corpus (20)

• Double Field Theory
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Non-Relativistic Gravity and its Coupling to Matter
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Extended Galilean symmetries of non-relativistic strings
• A Non-Relativistic Limit of NS-NS Gravity
• The Geometry, Branes and Applications of Exceptional Field Theory
• A worldsheet supersymmetric Newton-Cartan string
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Nonrelativistic Open String and Yang-Mills Theory
• A master exceptional field theory
• Non-relativistic duality and $T\bar{T}$ deformations
• Probing tachyon kinks in Newton-Cartan background
• Non-Riemannian isometries from double field theory
• Non-Riemannian gravity actions from double field theory
• Non-Relativistic M2-Brane
• p-brane Newton--Cartan Geometry

Cited by in corpus (20)

• Torsional string Newton-Cartan geometry for non-relativistic strings
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Dual D-Brane Actions in Nonrelativistic String Theory
• Unification of Decoupling Limits in String and M-theory
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Worldsheet Formalism for Decoupling Limits in String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Generalized Newton-Cartan Geometries for Particles and Strings
• Anisotropic Compactification of Nonrelativistic M-Theory
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Identifying Riemannian singularities with regular non-Riemannian geometry
• Nonrelativistic expansion of M2 branes and M theory backgrounds
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• How to Build a Black Hole out of Instantons
• de Sitter Holography and Carrollian Brane Theories
• Nonrelativistic expansion of type IIA NS5 brane