The authors compute the leading finite-size corrections to thermal observables of the large-N critical O(N) model on S^1 x S^2 using a perturbative expansion in beta/r.
$3d$ fermion-boson map with imaginary chemical potential
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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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The large $N$ vector model on $S^1\times S^2$
The authors compute the leading finite-size corrections to thermal observables of the large-N critical O(N) model on S^1 x S^2 using a perturbative expansion in beta/r.