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Aspects of chiral anomalies at finite density Metlitski, Max A.

Abstract

This thesis is devoted to the study of various aspects of chiral anomaly in an environment with a non-vanishing fermion density. It is comprised of 3 semi-autonomous projects. In the first part, we examine the problem of Witten's superconducting strings at finite fermion chemical potential. We demonstrate how various symmetries of the hamiltonian can be used to exactly compute the fermion electric current in the string background. We show that the current along the string is not sensitive to the profiles of the string fields, and at fixed chemical potential and temperature depends only on the string winding number, the total gauge flux through the vortex and, possibly, the fermion mass at infinity. In the second part, we study a complementary problem of appearance of axial current on magnetic flux tubes in dense matter. We demonstrate the appearance of the axial current by an explicit microscopic calculation. We further show how the results of both parts I and II can be derived by thinking of the fermion chemical potential as a background gauge field, which induces an anomaly of the axial current. In the third part, we use 2-color QCD as a model to study the effects of simultaneous presence of the so-called Ө parameter, chemical potentials for baryon number, μ[sub B] and for isospin charge, μ[sub I]. We pay special attention to Ө, μ[sub B], μ[sub I] dependence of different vacuum condensates, including chiral and diquark condensates, as well as the gluon condensate and the topological susceptibility. We find that two phase transitions of the second order will occur when Ө relaxes from Ө = 2π to Ө = 0, if μ is of order of the pion mass, m[sub π] . We demonstrate that the transition to the superfluid phase at Ө = π occurs at a much lower chemical potential than at Ө = 0. We also show that the strong Ө dependence present near Ө = π in vacuum (Dashen's phenomenon), becomes smoothed out in the superfluid phase. Finally, we note that all results of this study easily generalize to N[sub c] = 3 QCD at finite isospin chemical potential.

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