No abstract

We perform holographic renormalization for probe branes in AdS 5 × S 5 . We show that for four known probe D-branes wrapping an AdS m × S n , the counterterms needed to render the action finite are identical to those for the free, massive scalar in AdS m plus counterterms for the renormalization of the volume of AdS m . The four cases we consider are the probe D7, two different probe D5's and a probe D3. In the D7 case there are schemedependent finite counterterms that can be fixed by supersymmetry.

We numerically construct asymptotically Anti-de Sitter charged black hole solutions of (4 + 1)-dimensional SU (2) Einstein-Yang-Mills theory that, for sufficiently low temperature, develop vector hair. Via gauge-gravity duality, these solutions describe a strongly-coupled conformal field theory at finite temperature and density that undergoes a phase transition to a superfluid state with spontaneously broken rotational symmetry (a p-wave superfluid state). The bulk theory has a single free parameter, the ratio of the five-dimensional gravitational constant to the Yang-Mills coupling, which we denote as α. Previous analyses have shown that in the so-called probe limit, where α goes to zero and hence the gauge fields are ignored in Einstein's equation, the transition to the superfluid state is second order. We construct fully back-reacted solutions, where α is finite and the gauge fields are included in Einstein's equation, and find that for values of α above a critical value α c = 0.365 ± 0.001 in units of the AdS radius, the transition becomes first order.

A conformal field theory (CFT) in dimension d ≥ 3 coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" b that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that b must decrease or remain constant from ultraviolet to infrared. Our result applies also to a CFT in d = 3 flat space with a planar boundary.

We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo effect is the screening of a magnetic impurity coupled anti-ferromagnetically to a bath of conduction electrons at low temperatures. In a (1+1)-dimensional CFT description, the Kondo effect is a renormalization group flow triggered by a marginally relevant (0+1)-dimensional operator between two fixed points with the same Kac-Moody current algebra. In the large-N limit, with spin SU (N ) and charge U (1) symmetries, the Kondo effect appears as a (0+1)-dimensional second-order mean-field transition in which the U (1) charge symmetry is spontaneously broken. Our holographic model, which combines the CFT and large-N descriptions, is a Chern-Simons gauge field in (2+1)-dimensional AdS space, AdS 3 , dual to the Kac-Moody current, coupled to a holographic superconductor along an AdS 2 subspace. Our model exhibits several characteristic features of the Kondo effect, including a dynamically generated scale, a resistivity with power-law behavior in temperature at low temperatures, and a spectral flow producing a phase shift. Our holographic Kondo model may be useful for studying many open problems involving impurities, including for example the Kondo lattice problem.