Topological invariants for holographic semimetals

We study the behavior of fermion spectral functions for the holographic topological Weyl and nodal line semimetals. We calculate the topological invariants from the Green functions of both holographic semimetals using the topological Hamiltonian method, which calculates topological invariants of strongly interacting systems from an effective Hamiltonian system with the same topological structure. Nontrivial topological invariants for both systems have been obtained and the presence of nontrivial topological invariants further supports the topological nature of the holographic semimetals.Comment: 39 pages, 11 figures, 1 table; v2: match published versio

Topological nodal line semimetals in holography

We show a holographic model of a strongly coupled topological nodal line semimetal (NLSM) and find that the NLSM phase could go through a quantum phase transition to a topologically trivial state. The dual fermion spectral function shows that there are multiple Fermi surfaces each of which is a closed nodal loop in the NLSM phase. The topological structure in the bulk is induced by the IR interplay between the dual mass operator and the operator that deforms the topology of the Fermi surface. We propose a practical framework for building various strongly coupled topological semimetals in holography, which indicates that at strong coupling topologically nontrivial semimetal states generally exist.Comment: 21 pages, 5 figures; v2: match published versio

Transport Coefficients from Extremal Gauss-Bonnet Black Holes

We calculate the shear viscosity of strongly coupled field theories dual to Gauss-Bonnet gravity at zero temperature with nonzero chemical potential. We find that the ratio of the shear viscosity over the entropy density is $1/4\pi$, which is in accordance with the zero temperature limit of the ratio at nonzero temperatures. We also calculate the DC conductivity for this system at zero temperature and find that the real part of the DC conductivity vanishes up to a delta function, which is similar to the result in Einstein gravity. We show that at zero temperature, we can still have the conclusion that the shear viscosity is fully determined by the effective coupling of transverse gravitons in a kind of theories that the effective action of transverse gravitons can be written into a form of minimally coupled scalars with a deformed effective coupling.Comment: 23 pages, no figure; v2, refs added; v3, more refs added; v4, version to appear in JHE

Shear Viscosity from the Effective Coupling of Gravitons

We review the progress in the holographic calculation of shear viscosity for strongly coupled field theories. We focus on the calculation of shear viscosity from the effective coupling of transverse gravitons and present some explicit examples.Comment: 10 pages, invited presentation for the 9th Asia-Pacific International Conference On Gravitation And Astrophysics (ICGA 9), June 28-July 2, 2009, Wuhan, China; for the proceedings to be published by World Scientifi

BCS instabilities of electron stars to holographic superconductors

We study fermion pairing and condensation towards an ordered state in strongly coupled quantum critical systems with a holographic AdS/CFT dual. On the gravity side this is modeled by a system of charged fermion interacting through a BCS coupling. At finite density such a system has a BCS instability. We combine the relativistic version of mean-field BCS with the semi-classical fluid approximation for the many-body state of fermions. The resulting groundstate is the AdS equivalent of a charged neutron star with a superconducting core. The spectral function of the fermions confirms that the ground state is ordered through the condensation of the pair operator. A natural variant of the BCS star is shown to exist where the gap field couples Stueckelberg-like to the AdS Maxwell field. This enhances the tendency of the system to superconduct.Comment: 35 pages, 8 figures; v2, minor change, published versio

Bose-Fermi competition in holographic metals

We study the holographic dual of a finite density system with both bosonic and fermionic degrees of freedom. There is no evidence for a universal bose-dominated ground state. Instead, depending on the relative conformal weights the preferred groundstate is either pure AdS-Reissner-Nordstrom, a holographic superconductor, an electron star, or a novel mixed state that is best characterized as a hairy electron star.Comment: 28 pages, 14 figures; v2, ref added, version to appear in JHE

Anomalous magnetoconductivity and relaxation times in holography

We study the magnetoconductivity induced by the axial anomaly via the chiral magnetic effect in strongly coupled holographic models. An important ingredient in our models is that the axial charge is non-conserved beyond the axial anomaly. We achieve this either by explicit symmetry breaking via a non-vanishing non-normalisable mode of an axially charged scalar or using a Stuckelberg field to make the AdS-bulk gauge field massive. The DC magnetoconductivites can be calculated analytically. They take a universal form in terms of gauge field mass at the horizon and quadratic dependence on the magnetic field. The axial charge relaxation time grows linearly with magnetic field in the large $B$ regime. Most strikingly positive magnetoconductivity is still present even when the relaxation times are short $\tau_5 \approx 1/(\pi T)$ and the axial charge can not be thought of as an approximate symmetry. In the $U(1)_A$ explicit breaking model, we also observe that the axial magnetic conductivity in the limit of strong symmetry breaking approaches the same universal value as for anomalous holographic superconductors in the zero temperature limit.Comment: 44 pages, 12 figures; v2: refs added, sec. 2.3 expande