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This thesis investigates the charged moments and the symmetry-resolved
entanglement entropy in the context of the AdS3/CFT2 duality. In the
first part, I focus on the holographic U(1) Chern-Simons-Einstein gravity,
a toy model of AdS3/CFT2 with U(1) Kac-Moody symmetry. I
start with the vacuum background with a single entangling interval. I
show that, apart from a partition function in the grand canonical ensemble,
the charged moments can also be interpreted as the two-point
function of vertex operators on the replica surface. For the holographic
description, I propose a duality between the bulk U(1) Wilson line and
the boundary vertex operators. I verify this duality by deriving the
effective action for the Chern-Simons fields and comparing the result
with the vertex correlator. In the twist field approach, I show that the
charged moments are given by the correlation function of the charged
twist operators and the additional background operators. To solve the
correlation functions involved, I prove the factorization of the U(1) extended
conformal block into a U(1) block and a Virasoro block. The
general expression for the U(1) block is derived by directly summing
over the current descendant states, and the result shows that it takes
an identical form as the vertex correlators. This leads to the conclusion
that the disjoint Wilson lines compute the neutral U(1) block. The final
result for the symmetry-resolved entanglement entropy shows that
it is always charge-independent in this model. In the second part, I
study charged moments in higher spin holography, where the boundary
theory is a CFT with W3 symmetry. I define the notion of the
higher spin charged moments by introducing a spin-3 modular charge
operator. Restricting to the vacuum background with a single entangling
interval, I employ the grand canonical ensemble interpretation
and calculate the charged moments via the known higher spin black
hole solution. On the CFT side, I perform a perturbative expansion for
the higher spin charged moments in terms of the connected correlation
functions of the spin-3 modular charge operators. Using the recursion
relation for the correlation functions of the W3 currents, I evaluate the
charged moments up to the quartic order of the chemical potential. The
final expression matches with the holographic result. My results both
for U(1) Chern-Simons Einstein gravity and W3 higher spin gravity
constitute novel checks of the AdS3/CFT2 correspondence.