Emergent Schrödinger geometries from mass-deformed CFT

Abstract

We study an M-theory solution for the holographic flow of AdS 4 times Sasaki-Einstein 7-manifolds with skew-whiffing, perturbed by a mass operator. The infrared solution contains the 5 dimensional Schrödinger geometry after considering the gravity dual of the standard non-relativistic limit of relativistic field theories. The mass deformation of the field theory is discussed in detail for the case with 7 manifold being a round sphere.

Bosonic fractionalisation transitions

“…Of course, solving the full equations coming from (4.1) order by order will determine the exact solution and thus distinguish between the two cases. This was pointed out earlier in [30].…”

“…In fact it approaches a zero-density state with vanishing (direct) conductivity. Furthermore, the T → 0 limit of the neutral and charged solutions meet at the unique, unbroken T = 0 solution of the system, which lifts to an eleven-dimensional Schrödinger solution of M-theory [30]. Thus the entire region 6 at T = 0 outside the dome is degenerate on a constant-µ phase diagram.…”

Finite temperature aging holography

“…There also have been efforts constructing Schrödinger solutions from string or M theory, sometimes with supersymmetry. See [21,22,23,24,25], for example. While these Schrödinger backgrounds have been drawn much interest, the progresses directly along this line have been hindered due to the conceptual difficulties related to their non-trivial boundary structures.…”

Flows to Schrödinger geometries

“…The metric of a gravity background dual to the boundary theories with Schrödinger 1 More general reductions, including these, are considered in [20,21]. 2 In a different context, flow solutions from AdS 4 spacetime to the five-dimensional Schrödinger geometry have been constructed in M-theory in [22], whose IR geometry was obtained in [23]. See also [24,25] for some related works on the geometric realization of Schrödinger symmetry.…”

“…We first consider the IIB SUGRA case, where d = 2 and the domain-wall solution we focus on has z = 2. We can solve (22) to obtain a fake superpotential, as shown in Fig. 1, which corresponds to the RG flow induced by the scalar source η (0) in the UV and flowing to the vacuum at η = η * in the IR.…”