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

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.

19 pages

References in corpus (5)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Particle-Vortex Duality from 3d Bosonization
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Bosonization and Mirror Symmetry
• How to get from imaginary to real chemical potential

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• Sharp disentanglement in holographic charged local quench
• The thermal representation of conformal ladder integrals