  We present a thorough analysis of the entanglement entropies related to
different symmetry sectors of free quantum field theories (QFT) with an
internal U(1) symmetry. We provide explicit analytic computations for the
charged moments of Dirac and complex scalar fields in two spacetime dimensions,
both in the massive and massless cases, using two different approaches. The
first one is based on the replica trick, the computation of the partition
function on Riemann surfaces with the insertion of a flux $\alpha$, and the
introduction of properly modified twist fields, whose two-point function
directly gives the scaling limit of the charged moments. With the second
method, the diagonalisation in replica space maps the problem to the
computation of a partition function on a cut plane, that can be written exactly
in terms of the solutions of non-linear differential equations of the
Painlev\'e V type. Within this approach, we also derive an asymptotic expansion
for the short and long distance behaviour of the charged moments. Finally, the
Fourier transform provides the desired symmetry resolved entropies: at the
leading order, they satisfy entanglement equipartition and we identify the
subleading terms that break it. Our analytical findings are tested against
exact numerical calculations in lattice models.

High Energy Physics - Theory;Statistical Mechanics