Andy O'Bannon

Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects

We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For boundary CFTs and DCFTs dual holographically to Einstein gravity theories, the thermal entropy is equivalent to the Bekenstein–Hawking entropy of a hyperbolic black brane. We show that the horizon of the hyperbolic black brane coincides with the minimal area surface used in Ryu and Takayanagi’s conjecture for the holographic calculation of EE. We thus prove their conjecture in these cases. We use our results to compute the Renyi entropies and EE in DCFTs in which the defect corresponds to a probe brane in a holographic dual.

On Holographic Defect Entropy

A bstractWe study a number of (3 + 1)- and (2 + 1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3 + 1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1 + 1)-dimensional field theories generalizes to higher dimensions.

Holographic impurities and Kondo effect

Magnetic impurities are responsible for many interesting phenomena in condensed matter systems, notably the Kondo effect and quantum phase transitions. Here we present a holographic model of a magnetic impurity that captures the main physical properties of the large-spin Kondo effect. We estimate the screening length of the Kondo cloud that forms around the impurity from a calculation of entanglement entropy and show that our results are consistent with the g-theorem.

Two-point functions in a holographic Kondo model

A bstractWe develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator O

Holographic Wilson Loops, Dielectric Interfaces, and Topological Insulators

\mathcal{O}

Transport and zero sound in holographic strange metals

built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form O†O

Constraint on Defect and Boundary Renormalization Group Flows.

{\mathcal{O}}^{\dagger}\mathcal{O}