Assuming that the AdS/CFT prescription is valid in the case of noncausal backgrounds, we apply it to the simplest possible eternal time machine solution in AdS 3 based on two conical defects moving around their center of mass along a circular orbit. Closed timelike curves in this space-time extend all the way to the boundary of AdS 3 , violating causality of the boundary field theory. By use of the geodesic approximation we address the issue of self-consistent dynamics of the dual 1 þ 1 dimensional field theory when causality is violated, and calculate the two-point retarded Green function. It has a nontrivial analytical structure both at negative and positive times, providing us with an intuition on how an interacting quantum field could behave once causality is broken.

We consider the planar local patch approximation of d = 2 fermions at finite density coupled to a critical boson. In the quenched or Bloch-Nordsieck approximation, where one takes the limit of fermion flavors N f → 0, the fermion spectral function can be determined exactly. We show that one can obtain this non-perturbative answer thanks to a specific identity of fermionic two-point functions in the planar local patch approximation. The resulting spectrum is that of a non-Fermi liquid: quasiparticles are not part of the exact fermionic excitation spectrum of the theory. Instead one finds continuous spectral weight with power law scaling excitations as in a d = 1 dimensional critical state. Moreover, at low energies there are three such excitations at three different Fermi surfaces, two with a low energy Green's function G ∼ (ω − v * k) −1/2 and one with G ∼ |ω + k| −1/3 .

We study a model in 1+2 dimensions composed of a spherical Fermi surface of N f flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion n-point functions of this theory in the limit N f → 0 followed by k F → ∞ where k F sets both the size and curvature of the Fermi surface. Using this framework we calculate the zero-temperature fermion density-density correlation function in real space and find an exponential decay of Friedel oscillations.

We show that the fermionic and bosonic spectrum of d = 2 fermions at finite density coupled to a critical boson can be determined nonperturbatively in the combined limit k F → ∞, N f → 0 with N f k F fixed. In this double scaling limit, the boson two-point function is corrected but only at one loop. This double scaling limit therefore incorporates the leading effect of Landau damping. The fermion two-point function is determined analytically in real space and numerically in (Euclidean) momentum space. The resulting spectrum is discontinuously connected to the quenched N f → 0 result. For ω → 0 with k fixed the spectrum exhibits the distinct non-Fermi-liquid behavior previously surmised from the RPA approximation. However, the exact answer obtained here shows that the RPA result does not fully capture the IR of the theory.