We formulate a linear response theory of the chiral magnetic effect in a finite Weyl semimetal, expressing the electrical current density j induced by a slowly oscillating magnetic field B or chiral chemical potential μ in terms of the scattering matrix of Weyl fermions at the Fermi level. Surface conduction can be neglected in the infinite-system limit for d dm j , but not for d d j B: the chirally circulating surface Fermi arcs give a comparable contribution to the bulk Weyl cones no matter how large the system is, because their smaller number is compensated by an increased flux sensitivity. The Fermi arc contribution to m d d j B 1 has the universal value ( ) e h 2 , protected by chirality against impurity scattering-unlike the bulk contribution of opposite sign.

Since any non-trivial infrared dynamics in strongly correlated electron matter must be controlled by a critical fixed point, we argue that the form of the single-particle propagator can be deduced simply by imposing scale invariance. As a consequence, the unparticle picture proposed by Georgi[1] is the natural candidate to describe such dynamics. Unparticle stuff is scale-invariant matter with no particular mass. Scale invariance dictates that the propagator has an algebraic form which can admit zeros and hence is a candidate to explain the ubiquitous pseudogap state of the cuprates. The non-perturbative electronic state formed out of unparticles we refer to as an un-Fermi liquid. We show that the underlying action of the continuous mass formulation of unparticles can be recast as an action in anti de Sitter space which serves as the generating functional for the propagator. We find that this mapping fixes the scaling dimension of the unparticle to be dU = d/2 + √ d 2 + 4/2 and ensures that the corresponding propagator has zeros with d the spacetime dimension of the unparticle field. Should d = 2 + 1, unparticles acquire the non-trivial phase 2πdU upon interchange. Because dU is non-integer and in general not half-integer, clockwise and counterclockwise interchange of unparticles do not lead to the same phase and time reversal symmetry is broken spontaneously as reported in numerous experiments in the pseudogap phase of the cuprates. The possible relevance of this mechanism to such experiments is discussed. We then formulate the analogous BCS gap using unparticles and find that in contrast to the Fermi liquid case, the transition temperature increases as the attractive interaction strength decreases, indicating that unparticles are highly susceptible to a superconducting instability.

We study real time correlators in strongly coupled N = 4 supersymmetric Yang-Mills theory on dS 3 × S 1 , with antiperiodic boundary conditions for fermions on the circle. When the circle radius is larger than a critical value, the dual geometry is the so-called "topological AdS 5 black hole". Applying the Son-Starinets recipe in this background we compute retarded glueball propagators which exhibit an infinite set of poles yielding the quasinormal frequencies of the topological black hole. The imaginary parts of the propagators exhibit thermal effects associated with the Gibbons-Hawking temperature due to the cosmological horizon of the de Sitter boundary. We also obtain R-current correlators and find that after accounting for a small subtlety, the Son-Starinets prescription yields the retarded Green's functions. The correlators do not display diffusive behaviour at late times. Below the critical value of the circle radius, the topological black hole decays to the AdS 5 "bubble of nothing". Using a high frequency WKB approximation, we show that glueball correlators in this phase exhibit poles on the real axis. The tunnelling from the black hole to the bubble is interpreted as a hadronization transition.

The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated metal with all-to-all random interactions (average strength J) between N fermions (complex Dirac fermions or real Majorana fermions). In the large-N limit a conformal symmetry emerges that renders the model exactly soluble. Here we study how the non-Fermi liquid behavior of the closed system in equilibrium manifests itself in an open system out of equilibrium. We calculate the current-voltage characteristic of a quantum dot, described by the complex-valued SYK model, coupled to a voltage source via a single-channel metallic lead (coupling strength Γ). A one-parameter scaling law appears in the large-N conformal regime, where the differential conductance G = dI/dV depends on the applied voltage only through the dimensionless combination ξ = eV J/Γ 2 . Low and high voltages are related by the duality G(ξ) = G(π/ξ). This provides for an unambiguous signature of the conformal symmetry in tunneling spectroscopy.

In charged current weak interaction processes, neutrinos are produced in an entangled state with the charged lepton. This correlated state is disentangled by the measurement of the charged lepton in a detector at the production site. We study the dynamical aspects of disentanglement, propagation and detection, in particular the conditions under which the disentangled state is a coherent superposition of mass eigenstates. The appearance and disappearance far-detection processes are described from the time evolution of this disentangled "collapsed" state. The familiar quantum mechanical interpretation and factorization of the detection rate emerges when the quantum state is disentangled on time scales much shorter than the inverse oscillation frequency, in which case the final detection rate factorizes in terms of the usual quantum mechanical transition probability provided the final density of states is insensitive to the neutrino energy difference. We suggest possible corrections for short-baseline experiments. If the charged lepton is unobserved, neutrino oscillations and coherence are described in terms of a reduced density matrix obtained by tracing out an un-observed charged lepton. The diagonal elements in the mass basis describe the production of mass eigenstates whereas the off diagonal ones provide a measure of coherence. It is shown that coherences are of the same order of the diagonal terms on time scales up to the inverse oscillation frequency, beyond which the coherences oscillate as a result of the interference between mass eigenstates.