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

TL;DR

This paper develops a non-relativistic string theory framework within the AdS/CFT correspondence, revealing a new holographic duality between non-relativistic strings and Spin Matrix theory near BPS bounds.

Contribution

It introduces a Polyakov-type action for non-relativistic strings in torsional Newton-Cartan geometry and connects it to Spin Matrix theory limits in AdS/CFT, expanding the understanding of non-relativistic holography.

Findings

Derivation of a non-relativistic string action in torsional Newton-Cartan geometry.

Identification of a scaling limit leading to Galilean conformal symmetry.

Establishment of a duality between non-relativistic strings and Spin Matrix theory.

Abstract

We find a Polyakov-type action for strings moving in a torsional Newton-Cartan geometry. This is obtained by starting with the relativistic Polyakov action and fixing the momentum of the string along a non-compact null isometry. For a flat target space, we show that the world-sheet theory becomes the Gomis-Ooguri action. From a target space perspective these strings are non-relativistic but their world-sheet theories are still relativistic. We show that one can take a scaling limit in which also the world-sheet theory becomes non-relativistic with an infinite-dimensional symmetry algebra given by the Galilean conformal algebra. This scaling limit can be taken in the context of the AdS/CFT correspondence and we show that it is realized by the `Spin Matrix Theory' limits of strings on AdS$_5$ $\times$ $S^5$. Spin Matrix theory arises as non-relativistic limits of the AdS/CFT correspondence close to BPS bounds. The duality between non-relativistic strings and Spin Matrix theory provides a holographic duality of its own and points towards a framework for more tractable holographic dualities whereby non-relativistic strings are dual to near BPS limits of the dual field theory.