Title: Finite-Size Effects in Non-Neutral Two-Dimensional Coulomb Fluids,
Abstract: Thermodynamic potential of a neutral two-dimensional (2D) Cou\-lomb fluid,
confined to a large domain with a smooth boundary, exhibits at any (inverse)
temperature $\beta$ a logarithmic finite-size correction term whose universal
prefactor depends only on the Euler number of the domain and the conformal
anomaly number $c=-1$. A minimal free boson conformal field theory, which is
equivalent to the 2D symmetric two-component plasma of elementary $\pm e$
charges at coupling constant $\Gamma=\beta e^2$, was studied in the past. It
was shown that creating a non-neutrality by spreading out a charge $Q e$ at
infinity modifies the anomaly number to $c(Q,\Gamma) = - 1 + 3\Gamma Q^2$.
Here, we study the effect of non-neutrality on the finite-size expansion of the
free energy for another Coulomb fluid, namely the 2D one-component plasma
(jellium) composed of identical pointlike $e$-charges in a homogeneous
background surface charge density. For the disk geometry of the confining
domain we find that the non-neutrality induces the same change of the anomaly
number in the finite-size expansion. We derive this result first at the
free-fermion coupling $\Gamma\equiv\beta e^2=2$ and then, by using a mapping of
the 2D one-component plasma onto an anticommuting field theory formulated on a
chain, for an arbitrary coupling constant.