Nonrelativistic String Theory in Background Fields

Abstract

Nonrelativistic string theory is a unitary, ultraviolet finite quantum gravity theory with a nonrelativistic string spectrum. The vertex operators of the worldsheet theory determine the spacetime geometry of nonrelativistic string theory, known as the string Newton-Cartan geometry. We compute the Weyl anomaly of the nonrelativistic string worldsheet sigma model describing strings propagating in a string Newton-Cartan geometry, Kalb-Ramond and dilaton background. We derive the equations of motion that dictate the backgrounds on which nonrelativistic string theory can be consistently defined quantum mechanically. The equations of motion we find from our study of the conformal anomaly of the worldsheet theory are to nonrelativistic string theory what the (super)gravity equations of motion are to relativistic string theory.

arXiv comment32 pages; v2: minor clarifications, fixed typos, references added; v3: a reference added

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• A worldsheet supersymmetric Newton-Cartan string
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• Generalized Newton-Cartan Geometries for Particles and Strings
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
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• Nonrelativistic expansion of M2 branes and M theory backgrounds
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• Dual Non-Lorentzian Backgrounds for Matrix Theories
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• KLT Factorization of Winding String Amplitudes
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Stable and Unstable Dp-branes in p-brane Newton-Cartan Background
• D-Brane Actions in Non-Relativistic String Theory and T-Duality
• A perturbative approach to the non-relativistic string spectrum
• Newton-Cartan $D0$ branes from $D1$ branes and integrability
• A new approach for nonrelativistic bosonic string in flat space time
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• Holographic duals of $\mathcal{N}=1$ quivers in 5d and their nonrelativistic limits