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.

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

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• 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