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Topological currents in dense matter Charbonneau, Arthur James


This thesis introduces the idea of a topological current that flows in regions with large magnetic fields, dense matter, and parity violation. We propose that such a current exists in the cores of neutron stars and may be responsible for the large proper motion (kicks) observed in some pulsars. This current is similar to the charge separation effect and chiral magnetic effect that may be responsible for parity (℘) and charge conjugation-parity (C℘) violation observed at the Relativistic Heavy Ion Collider (RHIC). We start by deriving the topological current two ways. The first is a macroscopic derivation where we appeal to an anomaly induced by the presence of a fictitious axial field. The second method is microscopic, in which we consider how the modes of the Dirac equation in a magnetic field and chemical potential contribute to the current. We then discuss in great detail the elements necessary for a topological current to exist in a dense star. Our concern then rests with calculating the magnitude of topological currents in the many phases of matter thought to exist in dense stars. We choose four representative processes to investigate: nuclear matter, hyperons, kaon condensates, and strange quark matter. We then suppose that this current may somehow transfer its momentum out of the star, either by being physically ejected or by emitting radiation, causing a kick. We also discuss how the current may induce magnetic helicity and a toroidal magnetic field in the core of the star. We end by discussing the topological current in terms of the AdS/CFT correspondence, a powerful tool that allows one to obtain results from strongly coupled field theories by transferring the problem to the language of a weakly coupled gravitational theory. We introduce a toy model to how one might introduce topological currents into the AdS/CFT framework.

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