Bending branes for DCFT in two dimensions

We consider a holographic dual model for defect conformal field theories (DCFT) in which we include the backreaction of the defect on the dual geometry. In particular, we consider a dual gravity system in which a two-dimensional hypersurface with matter fields, the brane, is embedded into a three-dimensional asymptotically Anti-de Sitter spacetime. Motivated by recent proposals for holographic duals of boundary conformal field theories (BCFT), we assume the geometry of the brane to be determined by Israel junction conditions. We show that these conditions are intimately related to the energy conditions for the brane matter fields, and explain how these energy conditions constrain the possible geometries. This has implications for the holographic entanglement entropy in particular. Moreover, we give exact analytical solutions for the case where the matter content of the brane is a perfect fluid, which in a particular case corresponds to a free massless scalar field. Finally, we describe how our results may be particularly useful for extending a recent proposal for a holographic Kondo model.Comment: 35 pages + appendices, 12 figures, v2: added references and a paragraph on negative tension solutions, v3: updated reference

Quantum Quenches in a Holographic Kondo Model

We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with $SU(N)$ spin. At large $N$, it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS$_2$ and models the impurity screening. We study the time dependence of the condensate induced by quenches of the Kondo coupling. The timescale for equilibration is generically given by the lowest-lying quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large $N$ phase transition, we study the critical slowing down and obtain the combination of critical exponents $z\nu=1$. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form $\sim t^{-a}\sin(b\log t)$. This indicates the emergence of a discrete scale invariance.Comment: 23 pages + appendices, 11 figure