Gravity dual of a multilayer system

Abstract

We construct a gravity dual to a system with multiple (2 + 1)-dimensional layers in a (3 + 1)-dimensional ambient theory. Following a top-down approach, we generate a geometry corresponding to the intersection of D3-and D5-branes along 2+1 dimensions. The D5-branes create a codimension one defect in the worldvolume of the D3-branes and are homogeneously distributed along the directions orthogonal to the defect. We solve the fully backreacted ten-dimensional supergravity equations of motion with smeared D5-brane sources. The solution is supersymmetric, has an intrinsic mass scale, and exhibits anisotropy at short distances in the gauge theory directions. We illustrate the running behavior in several observables, such as Wilson loops, entanglement entropy, and within thermodynamics of probe branes.

Holographic spontaneous anisotropy

“…To find these backreacted geometries we will follow the smearing approach (see [68] for a review) and will homogeneously distribute the D5-branes in such a way that a residual amount of supersymmetry is preserved. The general form of the smeared type IIB backgrounds corresponding to the D3-D5 array in (2.1) was found in [69] (see also [54,55]). To write the deformed metric, let us represent the five-sphere S 5 as a U (1) bundle over CP 2 .…”

“…Since supersymmetry will be broken, it is to be expected that stable configurations do not admit an arbitrary distribution of smeared branes, but rather that it will be unique or very constrained, if it exists. In this work we have focused on duals to states with spontaneously broken isotropy, but our identification of the dual operator sourced by the branes as an axial current connects the multilayered solutions of [54][55][56] to the physics of Weyl semimetals (see, e.g., [85]), although in the last case the axial current is Abelian. It is clearly interesting to pursue this direction further.…”

“…The preservation of two supercharges for our Ansatz leads to a series of first-order differential equations for the functions in (2.2). These equations can be combined and reduced to single second-order equation for a master function W (ζ) [55,69], in terms of which f and φ are given by…”

“…In this appendix we flesh out more details of the family of backgrounds found in [54,55,69] and generalize in the current context. Besides the metric and the dilaton written in (2.2) and (2.3), these backgrounds of type IIB supergravity contain a RR five-form F 5 and a RR three-form F 3 .…”

“…The D5-branes are smeared along the transverse directions parallel to the D3-branes, in such a way that the resulting solution is homogeneous but anisotropic along one of the spatial directions of the field theory dual. Configurations of this type were previously constructed and studied in [54][55][56]. The main novelty in this work is that we allow the density of D5-branes to go to zero at the asymptotic boundary of space.…”