Multi-charged moments and symmetry-resolved R\'enyi entropy of free compact boson for multiple disjoint intervals

We study multi-charged moments and symmetry-resolved R\'enyi entropy of free compact boson for multiple disjoint intervals. The R\'enyi entropy evaluation involves computing the partition function of the theory on Riemann surfaces with genus g>1. This makes R\'enyi entropy sensitive to the local conformal algebra of the theory. The free compact boson possesses a global U(1) symmetry with respect to which we resolve R\'enyi entropy. The multi-charged moments are obtained by studying the correlation function of flux-generating vertex operators on the associated Riemann surface. Symmetry-resolved R\'enyi entropy is then obtained from the Fourier transforms of the charged moments. R\'enyi entropy is shown to have the familiar equipartition into local charge sectors up to the leading order. The multi-charged moments are also essential in studying the symmetry resolution of mutual information. The multi-charged moments of the self-dual compact boson and massless Dirac fermion are also shown to match for the cases when the associated reduced density matrix moments are known to be the same. Finally, we numerically check our results against the tight-binding model.