Nonrelativistic Approximations of Closed Bosonic String Theory

Abstract

We further develop the string $1/c^2$ expansion of closed bosonic string theory, where $c$ is the speed of light. The expansion will be performed up to and including the next-to-next-to-leading order (NNLO). We show that the next-to-leading order (NLO) theory is equal to the Gomis--Ooguri string, generalised to a curved target space, provided the target space geometry admits a certain class of co-dimension-2 foliations. We compute the energy of the string up to NNLO for a flat target space with a circle that must be wound by the string, and we show that it agrees with the $1/c^2$ expansion of the relativistic energy. We also compute the algebra of Noether charges for a flat target space and show that this matches order-by-order with an appropriate expansion of the Poincaré algebra, which at NLO gives the string Bargmann algebra. Finally, we expand the phase space action, which allows us to perform the Dirac procedure and pass to the quantum theory. It turns out that the Poisson brackets change at each order, and we show that the normal ordering constant of the relativistic theory, which does not depend on $c$, can be reproduced by the NLO and NNLO theories.

arXiv comment64 pages incl. 3 appendices, 2 figures; v2: updated to published version

References in corpus (60)

• Ambitwistor strings and the scattering equations
• Non-Relativistic Closed String Theory
• Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5
• Classical and Quantized Tensionless Strings
• IIA/B, Wound and Wrapped
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Action Principle for Newtonian Gravity
• `Stringy' Newton-Cartan Gravity
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Non-Relativistic Gravity and its Coupling to Matter
• Tensionless Strings from Worldsheet Symmetries
• On the null origin of the ambitwistor string
• String Theory and String Newton-Cartan Geometry
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Non-relativistic strings and branes as non-linear realizations of Galilei groups
• Relating non-relativistic string theories
• Non-Relativistic Superbranes
• Extended Galilean symmetries of non-relativistic strings
• Aspects of Nonrelativistic Strings
• Nonrelativistic String Theory in Background Fields
• Dynamics of Carroll Strings
• Torsional string Newton-Cartan geometry for non-relativistic strings
• Gravity between Newton and Einstein
• A Non-Relativistic Limit of NS-NS Gravity
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• Newtonian Gravitons and D-brane Collective Coordinates in Wound String Theory
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• Torsional Newton Cartan gravity from non-relativistic strings
• A worldsheet supersymmetric Newton-Cartan string
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• An Action for Extended String Newton-Cartan Gravity
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Torsional Deformation of Nonrelativistic String Theory
• Dual D-Brane Actions in Nonrelativistic String Theory
• Nonrelativistic Open String and Yang-Mills Theory
• T-Duality in Nonrelativistic Open String Theory
• Non-Riemannian geometry of M-theory
• Non-relativistic duality and $T\bar{T}$ deformations
• String Theory and non-Riemannian Geometry
• Probing tachyon kinks in Newton-Cartan background
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Nonrelativistic String Theory Sigma Model and Its Canonical Formulation
• Non-Riemannian isometries from double field theory
• Non Relativistic Dp Branes
• Non-Riemannian gravity actions from double field theory
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Symmetries of post-Galilean expansions
• Note About T-duality of Non-Relativistic String
• Non-Relativistic Superstring Theories
• p-brane Newton--Cartan Geometry
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• Non-Relativistic D-brane from T-duality Along Null Direction
• Coset space actions for nonrelativistic strings
• Extending the non-relativistic string AdS coset
• Decoding the Spin-Matrix limit of strings on $Ad{S}_5\times S^5$

Cited by in corpus (13)

• Worldsheet Formalism for Decoupling Limits in String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• The Panorama of Spin Matrix Theory
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• A coupling prescription for post-Newtonian corrections in Quantum Mechanics
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• A perturbative approach to the non-relativistic string spectrum
• Non-relativistic quantum strings from gauged WZW models
• Nonrelativistic expansion of type IIA NS5 brane
• Strings near BTZ black holes: A Carrollian Chronicle