Holographic spontaneous anisotropy

Abstract

Abstract We construct a family of holographic duals to anisotropic states in a strongly coupled gauge theory. On the field theory side the anisotropy is generated by giving a vacuum expectation value to a dimension three operator. We obtain our gravity duals by considering the geometry corresponding to the intersection of D3- and D5- branes along 2+1 dimensions. Our backgrounds are supersymmetric and solve the fully backreacted equations of motion of ten-dimensional supergravity with smeared D5-brane sources. In all cases the geometry flows to AdS 5 × 𝕊5 in the UV, signaling an isotropic UV fixed point of the dual field theory. In the IR, depending on the parameters of the solution, we find two possible behaviors: an isotropic fixed point or a geometry with anisotropic Lifshitz-like scaling symmetry. We study several properties of the solutions, including the entanglement entropy of strips. We show that any natural extension of existing c-functions will display non-monotonic behavior, conforming with the presence of new degrees of freedom only at intermediate regions between the boundary and the origin of the holographic dual.

Keywords

• AdS-CFT Correspondence
• D-branes
• Gauge-gravity correspondence
• Holography and condensed matter physics (AdS/CMT)