Non-Relativistic Strings and Limits of the AdS/CFT Correspondence

Abstract

Using target space null reduction of the Polyakov action we find a novel covariant action for strings moving in a torsional Newton-Cartan geometry. Sending the string tension to zero while rescaling the Newton-Cartan clock 1-form, so as to keep the string action finite, we obtain a non-relativistic string moving in a new type of non-Lorentzian geometry that we call $U(1)$-Galilean geometry. We apply this to strings on $Ad{S}_5\times S^5$ for which we show that the zero tension limit is realized by the Spin Matrix theory limits of the AdS/CFT correspondence. This is closely related to limits of spin chains studied in connection to integrability in AdS/CFT. The simplest example gives a covariant version of the Landau-Lifshitz sigma-model.

5 pages

References in corpus (5)

• Newtonian Gravity and the Bargmann Algebra
• Spacetime Symmetries of the Quantum Hall Effect
• Lifshitz Space-Times for Schroedinger Holography
• Extended Galilean symmetries of non-relativistic strings
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

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