A complex path around the sign problem

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues and present some results for low dimensional field theories in both imaginary and real time.Comment: Write up of the talk delivered al Lattice 201

Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice

We propose a method for the lattice QCD computation of nucleon-nucleon low-energy interactions. It consists in simulating QCD in the background of a ''electromagnetic" field whose potential is non-vanishing, but whose field strength is zero. By tuning the background field, phase-shifts at any (but small) momenta can be determined by measuring the shift of the ground state energy. Lattice sizes as small as 5 Fermi can be sufficient for the calculation of phase shifts up to momenta of order of $m_{\pi}/2$

Goldstone modes in the neutron star core

We formulate a theory of Goldstone bosons and their interactions in the superfluid and superconducting phase of dense nucleonic matter at densities of relevance to the neutron star core. For typical neutron star temperatures in the range T = 10^6 to 10^9 K, the Goldstone mode associated with rotational symmetry, called angulons, couple weakly to each other and to electrons. Consequently, these modes have anomalously large mean free paths and can contribute to both diffusive and ballistic transport of heat and momentum. In contrast, the two Goldstone bosons associated with density oscillations of the neutron and electron + proton fluids, called superfluid phonons, mix and couple strongly to electrons. They have shorter mean free paths, and their contribution to transport is negligible. Long-wavelength superfluid phonons and angulons can play a role in neutron star seismology, and lead to interesting phenomenology as angulons couple to magnetic fields and have anisotropic dispersion relations.Comment: 4 pages, 1 figur

How to Renormalize the Gap Equation in High Density QCD

We discuss two technical issues related to the gap equation in high-density QCD: i) how to obtain the asymptotic solution with well controlled approximations, and ii) the renormalization of four-quark operators in the high-density effective field theory.Comment: 8 pages, LaTeX, 1 eps figur