An Action for Extended String Newton-Cartan Gravity

Abstract

We construct an action for four-dimensional extended string Newton-Cartan gravity which is an extension of the string Newton-Cartan gravity that underlies nonrelativistic string theory. The action can be obtained as a nonrelativistic limit of the Einstein-Hilbert action in General Relativity augmented with a term that contains an auxiliary two-form and one-form gauge field that both have zero flux on-shell. The four-dimensional extended string Newton-Cartan gravity is based on a central extension of the algebra that underlies string Newton-Cartan gravity. The construction is similar to the earlier construction of a three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which is based on a central extension of the algebra that underlies Newton-Cartan gravity. We show that this three-dimensional action is naturally obtained from the four-dimensional action by a reduction over the spatial isometry direction longitudinal to the string followed by a truncation of the extended string Newton-Cartan gravity fields. Our construction can be seen as a special case of the construction of an action for extended p-brane Newton-Cartan gravity in p+3 dimensions.

arXiv comment16 pages; v2: references added; v3: 18 pages, published version

References in corpus (23)

• Galilean Conformal Algebras and AdS/CFT
• The exotic Galilei group and the "Peierls substitution"
• Non-Relativistic Closed String Theory
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Carroll versus Galilei Gravity
• `Stringy' Newton-Cartan Gravity
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Higher dimensional Chern-Simons supergravity
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Three-Dimensional Extended Bargmann Supergravity
• Non-relativistic strings and branes as non-linear realizations of Galilei groups
• Anyon spin and the exotic central extension of the planar Galilei group
• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Extended Galilean symmetries of non-relativistic strings
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Anyons from Strings
• Classical general relativity as BF-Plebanski theory with linear constraints
• Tachyons in the Galilean limit
• The Galilean Superstring
• Bulk-boundary correspondence between charged, anyonic strings and vortices

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• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• Torsional Newton Cartan gravity from non-relativistic strings
• A worldsheet supersymmetric Newton-Cartan string
• On the Non-Relativistic Expansion of Closed Bosonic Strings
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• Torsional Deformation of Nonrelativistic String Theory
• Oddity in nonrelativistic, strong gravity
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• Worldsheet Formalism for Decoupling Limits in String Theory
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• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Stringy (Galilei) Newton-Hooke Chern-Simons Gravities
• Non-relativistic $k$-contractions of the Coadjoint Poincaré algebra
• Nonrelativistic giant magnons from Newton Cartan strings
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