We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group
G and Chern-Simons level
k. We focus on the quantum states associated with the
Tdm,dn torus link complements, which is a
d-party pure quantum state, and analyze its large-party limit, i.e.,
d→∞ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of
ln∣ZG∣, where
∣ZG∣ is the order of the center of the group
G. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and
Td,dn torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical (
k→∞) limit of the entropies after taking the large-party limit for this particular example.
The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and non-Abelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the Abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the non-Abelian theory is computed in a gauge-invariant Gaussian approximation, which incorporates the dynamically generated mass gap. A formulation of the contact term for the non-Abelian case is also presented.