We study the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. As a result of electrostatic interactions between the instantons, this condensate expands towards the UV when the chemical potential is increased, giving a holographic version of the expansion of the Fermi surface. We argue based on properties of instantons that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density. This suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large N c QCD at asymptotically large chemical potential. We study properties of the nuclear matter phase as a function of chemical potential beyond the transition and argue in particular that the model can be used to make a semi-quantitative prediction of the binding energy per nucleon for nuclear matter in ordinary QCD.

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.

We describe the extension of the improvement program for bilinear operators composed of Wilson fermions to non-degenerate dynamical quarks. We consider two, three and four flavors, and both flavor non-singlet and singlet operators. We find that there are many more improvement coefficients than with degenerate quarks, but that, for three or four flavors, nearly all can be determined by enforcing vector and axial Ward identities. The situation is worse for two flavors, where many more coefficients remain undetermined.

We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m 2 π /(4πfπ) 2 ∼ aΛ (a being the lattice spacing, and Λ = ΛQCD). We then focus on the region where m 2 π /(4πfπ) 2 ∼ (aΛ) 2 , in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, we find two possible phase diagrams, depending on the sign of a coefficient in the chiral Lagrangian. For one sign, there is an Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is washed out into a crossover if the twisted mass is non-vanishing. For the other sign, there is a first order transition for pure Wilson fermions, and we find that this transition extends into the twisted mass plane, ending with two symmetrical second order points at which the mass of the neutral pion vanishes. We provide graphs of the condensate and pion masses for both scenarios, and note a simple mathematical relation between them. These results may be of importance to numerical simulations.

We calculate entanglement and impurity entropies in a recent holographic model of a magnetic impurity interacting with a strongly coupled system. There is an RG flow to an IR fixed point where the impurity is screened, leading to a decrease in impurity degrees of freedom. This information loss corresponds to a volume decrease in our dual gravity model, which consists of a codimension one hypersurface embedded in a BTZ black hole background in three dimensions. There are matter fields defined on this hypersurface which are dual to Kondo field theory operators. In the large N limit, the formation of the Kondo cloud corresponds to the condensation of a scalar field. The entropy is calculated according to the Ryu-Takayanagi prescription. This requires to determine the backreaction of the hypersurface on the BTZ geometry, which is achieved by solving the Israel junction conditions. We find that the larger the scalar condensate gets, the more the volume of constant time slices in the bulk is reduced, shortening the bulk geodesics and reducing the impurity entropy. This provides a new non-trivial example of an RG flow satisfying the g-theorem. Moreover, we find explicit expressions for the impurity entropy which are in agreement with previous field theory results for free electrons. This demonstrates the universality of perturbing about an IR fixed point.Dedicated to the memory of our colleague Peter Breitenlohner