3d fermion-boson map with imaginary chemical potential

We study the three-dimensional U(N) Gross-Neveu and CPN−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 fields in a monopole background. We show that the presence of the imaginary chemical potential for t...

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Bibliographic Details
Published in:Physical review. D 2017-03, Vol.95 (6), Article 065029
Main Authors: Filothodoros, Evangelos G., Petkou, Anastasios C., Vlachos, Nicholas D.
Format: Article
Language:English
Subjects:
Chemical potential
Free energy
Organic chemistry
Solid phases
Three dimensional models
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Summary:We study the three-dimensional U(N) Gross-Neveu and CPN−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 fields 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 mapping of the free energies involves the Bloch-Wigner function and its generalizations introduced by Zagier. We expect that our results are connected to the recently discussed 3d bosonization.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.95.065029