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In this paper, we revisit the computation of particle number fluctuations andthe R\'{e}nyi entanglement entropy of a two-dimensional Fermi gas usingmulti-dimensional bosonization. In particular, we compute these quantities fora circular Fermi surface and a circular entangling surface. Both quantitiesdisplay a logarithmic violation of the area law, and the R\'{e}nyi entropyagrees with the Widom conjecture. Lastly, we compute the symmetry-resolvedentanglement entropy for the two-dimensional circular Fermi surface and findthat, while the total entanglement entropy scales as $R\log R$, thesymmetry-resolved entanglement scales as $\sqrt{R\log R}$, where $R$ is theradius of the subregion of our interest.

Particle Number Fluctuations, R\'{e}nyi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization