Marginally deformed Schrödinger/dipole CFT correspondence

Abstract

We construct and thoroughly study a new integrable example of the AdS/CFT correspondence with Schrödinger symmetry. On the gravity side, the supergravity solution depends on two parameters and is obtained by marginally deforming the internal space of the Schrödinger 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. By using the Landau-Lifshitz coherent state Lagrangian, which originates from field theory, we reproduce the leading, in the deformation parameters, terms of the string theory prediction. This constitutes a non-trivial test of the correspondence. 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 Schrödinger parameter. When the separation length is much greater than the Schrödinger 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. This applies to operators of large length, for which finite size corrections are suppressed.