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arXiv · 1608.07795

$3d$ fermion-boson map with imaginary chemical potential

E. G. Filothodoros·A. C. Petkou·N. D. Vlachos
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Abstract

We study the three-dimensional $U(N)$ Gross-Neveu and CP$^{N-1}$ models in the canonical formalism with fixed $U(1)$ charge. For large-$N$ this is closely related to coupling the models to abelian Chern-Simons in a monopole background. We show that the presence of the imaginary chemical potential for the $U(1)$ charge makes the phase structure of the models remarkably similar. We calculate their respective large-$N$ free energy densities and show that they are mapped into each other in a precise way. Intriguingly, the free energy map involves the Bloch-Wigner function and its generalizations introduced by Zagier. We expect that our results are connected to the recently discussed $3d$ bosonization.

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E. G. Filothodoros, A. C. Petkou, N. D. Vlachos. 2016-08-28. $3d$ fermion-boson map with imaginary chemical potential. https://doi.org/10.1103/physrevd.95.065029

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