Marginally deformed Schr\"{o}dinger/dipole CFT correspondence

TL;DR

This paper constructs a new integrable AdS/CFT model with Schr"odinger symmetry, analyzing its gravity and field theory duals, and explores string solutions, Wilson loops, and spectra to understand its physical properties.

Contribution

It introduces a novel doubly deformed Schr"odinger background in AdS/CFT, providing explicit solutions, dual field theory identification, and spectral analysis to advance understanding of non-relativistic holography.

Findings

Derived a new supergravity solution with two deformation parameters.

Reproduced the dispersion relation using Landau-Lifshitz coherent states.

Calculated Wilson loops showing confining and conformal behaviors.

Abstract

We construct and thoroughly study a new integrable example of the AdS/CFT correspondence with Schr\"{o}dinger symmetry. On the gravity side, the supergravity solution depends on two parameters and is obtained by marginally deforming the internal space of the Schr\"{o}dinger background through a series of TsT transformations. On the field theory side, we identify the dual field theory which also depends on two parameters. We find a point-like string solution and derive its dispersion relation. A non-trivial test of the correspondence is provided by using the Landau-Lifshitz coherent state approach to reproduce the leading, in the deformation parameters, terms of that relation. Then, we calculate the Wilson loop, describing the quark/anti-quark potential at strong coupling. It exhibits confining behaviour when the separation length is much less than the Schr\"{o}dinger parameter. When the separation length is much greater than the Schr\"{o}dinger parameter the behaviour is that of a conformal theory. Subsequently, we take the Penrose limit along a certain null geodesic of the constructed background and calculate the bosonic spectrum. Based on that spectrum, we make an educated guess for the exact, in the 't Hooft coupling, dispersion relation of the magnon excitations in the original doubly deformed background. This provides us with an exact prediction for the dimensions of the dual field theory operators.